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Giles-Donovan N, Hillier AD, Ishida K, Hampshire BV, Giblin SR, Roessli B, Gehring PM, Xu G, Li X, Luo H, Cochran S, Stock C. Magnetic skin effect in Pb(Fe _{1/2}$Nb _{1/2}$)O 3. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:435802. [PMID: 39025119 DOI: 10.1088/1361-648x/ad6523] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2024] [Accepted: 07/18/2024] [Indexed: 07/20/2024]
Abstract
Relaxor-ferroelectrics display exceptional dielectric properties resulting from the underlying random dipolar fields induced by strong chemical inhomogeneity. An unusual structural aspect of relaxors is a skin-effect where the near-surface region in single crystals exhibit structures and critical phenomena that differ from the bulk. Relaxors are unique in that this skin effect extends over a macroscopic lengthscale of ∼100 μmwhereas usual surface layers only extend over a few unit cells (or ∼nm). We present a muon spectroscopy study of Pb(Fe_{1/2}Nb_{1/2})O3(PFN) which displays ferroelectric order, including many relaxor-like dielectric properties such as a frequency broadened dielectric response, and antiferromagnetism with spatially short-range polar correlations and hence can be termed a multiferroic. In terms of the magnetic behavior determined by the Fe3+(S=5/2,L ≈ 0) ions, PFN has been characterized as a unique example of a 'cluster spin-glass'. We use variable momentum muon spectroscopy to study the depth dependence of the slow magnetic relaxations in a large 1 cm3crystal of PFN. Zero-fieldpositivemuon spin relaxation is parameterized using a stretched exponential, indicative of a distribution of relaxation rates of the Fe3+spins. This bandwidth of frequencies changes as a function of muon momentum, indicative of a change in the Fe3+relaxation rates as a function of muon implantation depth in our single crystal. Usingnegativemuon elemental analysis, we find small-to-no measurable change in the Fe3+/Nb5+concentration with depth implying that chemical concentration alone cannot account for the change in the relaxational dynamics. PFN displays an analogous magnetic skin effect reported to exist in the structural properties of relaxor-ferroelectrics.
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Affiliation(s)
- N Giles-Donovan
- Centre for Medical and Industrial Ultrasonics, James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, United Kingdom
| | - A D Hillier
- ISIS Facility, Rutherford Appleton Laboratory, Harwell, Didcot, United Kingdom
| | - K Ishida
- ISIS Facility, Rutherford Appleton Laboratory, Harwell, Didcot, United Kingdom
- RIKEN Nishina Center, RIKEN, Wako, Saitama, Japan
| | - B V Hampshire
- ISIS Facility, Rutherford Appleton Laboratory, Harwell, Didcot, United Kingdom
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - S R Giblin
- School of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, United Kingdom
| | - B Roessli
- Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut (PSI), 5232 Villigen PSI, Switzerland
| | - P M Gehring
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899-6100, United States of America
| | - G Xu
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899-6100, United States of America
| | - X Li
- Chinese Academy of Sciences, Shanghai Institute of Ceramics, Shanghai, People's Republic of China
| | - H Luo
- Chinese Academy of Sciences, Shanghai Institute of Ceramics, Shanghai, People's Republic of China
| | - S Cochran
- Centre for Medical and Industrial Ultrasonics, James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, United Kingdom
| | - C Stock
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
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2
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Yao L, Jack RL. Heterogeneous nucleation in the random field Ising model. J Chem Phys 2023; 159:244110. [PMID: 38149735 DOI: 10.1063/5.0181596] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Accepted: 11/30/2023] [Indexed: 12/28/2023] Open
Abstract
We investigate the nucleation dynamics of the three-dimensional random field Ising model under an external field. We use umbrella sampling to compute the free-energy cost of a critical nucleus and use forward flux sampling for the direct estimation of nucleation rates. For moderate to strong disorder, our results indicate that the size of the nucleating cluster is not a good reaction coordinate, contrary to the pure Ising model. We rectify this problem by introducing a coordinate that also accounts for the location of the nucleus. Using the free energy barrier to predict the nucleation rate, we find reasonable agreement, although deviations become stronger as disorder increases. We attribute this effect to cluster shape fluctuations. We also discuss finite-size effects on the nucleation rate.
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Affiliation(s)
- Liheng Yao
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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3
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Fytas NG, Martín-Mayor V, Parisi G, Picco M, Sourlas N. Finite-size scaling of the random-field Ising model above the upper critical dimension. Phys Rev E 2023; 108:044146. [PMID: 37978671 DOI: 10.1103/physreve.108.044146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 10/05/2023] [Indexed: 11/19/2023]
Abstract
Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of statistical physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In the present manuscript we address this problem in the even more complicated case of disordered systems. In particular, we investigate the scaling behavior of the random-field Ising model at dimension D=7, i.e., above its upper critical dimension D_{u}=6, by employing extensive ground-state numerical simulations. Our results confirm the hypothesis that at dimensions D>D_{u}, linear length scale L should be replaced in finite-size scaling expressions by the effective scale L_{eff}=L^{D/D_{u}}. Via a fitted version of the quotients method that takes this modification, but also subleading scaling corrections into account, we compute the critical point of the transition for Gaussian random fields and provide estimates for the full set of critical exponents. Thus, our analysis indicates that this modified version of finite-size scaling is successful also in the context of the random-field problem.
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Affiliation(s)
- Nikolaos G Fytas
- Department of Mathematical Sciences, University of Essex, Colchester CO4 3SQ, United Kingdom
| | - Víctor Martín-Mayor
- Departamento de Física Téorica I, Universidad Complutense, 28040 Madrid, Spain
- Instituto de Biocomputacíon y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, P.le Aldo Moro 2, 00185 Rome, Italy and INFN, Sezione di Roma I, IPCF-CNR, P.le A. Moro 2, 00185 Rome, Italy
| | - Marco Picco
- Laboratoire de Physique Théorique et Hautes Energies, UMR7589, Sorbonne Université et CNRS, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Nicolas Sourlas
- Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (Unité Mixte de Recherche du CNRS et de l'Ecole Normale Supérieure, associée à l'Université Pierre et Marie Curie, PARIS VI) 24 rue Lhomond, 75231 Paris Cedex 05, France
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4
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d'Auriac JCA, Iglói F. Random-bond antiferromagnetic Ising model in a field. Phys Rev E 2022; 106:034117. [PMID: 36266800 DOI: 10.1103/physreve.106.034117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 08/29/2022] [Indexed: 06/16/2023]
Abstract
Using combinatorial optimization techniques we study the critical properties of the two- and three-dimensional Ising models with uniformly distributed random antiferromagnetic couplings (1≤J_{i}≤2) in the presence of a homogeneous longitudinal field, h, at zero temperature. In finite systems of linear size, L, we measure the average correlation function, C_{L}(ℓ,h), when the sites are either on the same sublattice, or they belong to different sublattices. The phase transition, which is of first order in the pure system, turns to mixed order in two dimensions with critical exponents 1/ν≈0.5 and η≈0.7. In three dimensions we obtain 1/ν≈0.7, which is compatible with the value of the random-field Ising model, but we cannot discriminate between second-order and mixed-order transitions.
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Affiliation(s)
| | - Ferenc Iglói
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary
- Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary
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5
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Joshi DC, Nordblad P, Mathieu R. Random fields and apparent exchange bias in the dilute Ising antiferromagnet Fe 0.6Zn 0.4F 2. Sci Rep 2020; 10:14588. [PMID: 32884093 PMCID: PMC7471909 DOI: 10.1038/s41598-020-71533-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Accepted: 08/17/2020] [Indexed: 11/08/2022] Open
Abstract
Random field induced spontaneous excess moments appear in field cooled single crystals of diluted Ising antiferromagnets. Here we report results from low temperature measurements of field cooled (including zero field) magnetic hysteresis loops parallel and perpendicular to the c-axis of a single crystal of composition Fe0.6Zn0.4F2. We find that weak static ferromagnetic excess moments attained on field cooling give rise to an apparent exchange bias of the magnetic hysteresis loops, whose magnitude is controlled by temperature and the strength and direction of the cooling field. Random field induced temporal excess moments only become observable in cooling fields larger than 1 T applied along the c-axis direction of the Fe0.6Zn0.4F2 single crystal.
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Affiliation(s)
- D C Joshi
- Department of Materials Science and Engineering, Uppsala University, Box 35, 751 03, Uppsala, Sweden.
| | - P Nordblad
- Department of Materials Science and Engineering, Uppsala University, Box 35, 751 03, Uppsala, Sweden
| | - R Mathieu
- Department of Materials Science and Engineering, Uppsala University, Box 35, 751 03, Uppsala, Sweden
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6
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Stock C, Songvilay M, Gehring PM, Xu G, Roessli B. Broadband critical dynamics in disordered lead-based perovskites. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:374012. [PMID: 32252031 DOI: 10.1088/1361-648x/ab86ee] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2019] [Accepted: 04/06/2020] [Indexed: 06/11/2023]
Abstract
Materials based on the cubic perovskite unit cell continue to provide the basis for technologically important materials with two notable recent examples being lead-based relaxor piezoelectrics and lead-based organic-inorganic halide photovoltaics. These materials carry considerable disorder, arising from site substitution in relaxors and molecular vibrations in the organic-inorganics, yet much of our understanding of these systems derives from the initial classic work of Prof. Roger A Cowley, who applied both theory and neutron scattering methods while at Chalk River Laboratories to the study of lattice vibrations in SrTiO3. Neutron scattering continues to play a vital role in characterizing lattice vibrations in perovskites owing to the simple cross section and the wide range of energy resolutions achievable with current neutron instrumentation. We discuss the dynamics that drive the phase transitions in the relaxors and organic-inorganic lead-halides in terms of neutron scattering and compare them to those in phase transitions associated with a 'central peak' and also a soft mode. We review some of the past experimental work on these materials and present new data from high-resolution time-of-flight backscattering spectroscopy taken on organic-inorganic perovskites. We will show that the structural transitions in disordered lead-based perovskites are driven by a broad frequency band of excitations.
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Affiliation(s)
- C Stock
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - M Songvilay
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - P M Gehring
- NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland, 20899, United States of America
| | - Guangyong Xu
- NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland, 20899, United States of America
| | - B Roessli
- Laboratory for Neutron Scattering and Imaging (LNS), Paul Scherrer Institute (PSI), 5232 Villigen PSI, Switzerland
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7
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Angelini MC, Lucibello C, Parisi G, Ricci-Tersenghi F, Rizzo T. Loop expansion around the Bethe solution for the random magnetic field Ising ferromagnets at zero temperature. Proc Natl Acad Sci U S A 2020; 117:2268-2274. [PMID: 31953263 PMCID: PMC7007560 DOI: 10.1073/pnas.1909872117] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We apply to the random-field Ising model at zero temperature ([Formula: see text]) the perturbative loop expansion around the Bethe solution. A comparison with the standard ϵ expansion is made, highlighting the key differences that make the expansion around the Bethe solution much more appropriate to correctly describe strongly disordered systems, especially those controlled by a [Formula: see text] renormalization group (RG) fixed point. The latter loop expansion produces an effective theory with cubic vertices. We compute the one-loop corrections due to cubic vertices, finding additional terms that are absent in the ϵ expansion. However, these additional terms are subdominant with respect to the standard, supersymmetric ones; therefore, dimensional reduction is still valid at this order of the loop expansion.
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Affiliation(s)
| | - Carlo Lucibello
- Artificial Intelligence Laboratory, Institute for Data Science and Analytics, Bocconi University, Milan 20136, Italy
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza University of Rome, Rome 00185, Italy;
- Sezione di Roma 1, Istituto Nazionale di Fisica Nucleare, Rome 00185, Italy
- Nanotec, Consiglio Nazionale delle Ricerche, Rome 00185, Italy
| | - Federico Ricci-Tersenghi
- Dipartimento di Fisica, Sapienza University of Rome, Rome 00185, Italy
- Sezione di Roma 1, Istituto Nazionale di Fisica Nucleare, Rome 00185, Italy
- Nanotec, Consiglio Nazionale delle Ricerche, Rome 00185, Italy
| | - Tommaso Rizzo
- Dipartimento di Fisica, Sapienza University of Rome, Rome 00185, Italy
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Rome 00185, Italy
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8
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Schmidt M, Romitti MV, Magalhaes SG, Zimmer FM. Field-induced glassy state in disordered cluster antiferromagnets. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:035805. [PMID: 31539890 DOI: 10.1088/1361-648x/ab469c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We investigate the role of antiferromagnetic spin clusters on the glassiness induced by uniform and random fields. We consider an antiferromagnetic disordered model that is treated within the replica method, resulting in an effective single-cluster problem. Our results show that regimes of weak and intermediate disorder are suitable for highly unusual phenomena. For the case of a uniform field, cluster polarization can favor a cluster spin-glass state, i.e. the magnetic field increases the freezing temperature at intermediate disorders. In addition, random fields introduce local perturbations that allow uncompensated cluster states, supporting cluster freezing even at very weak disorders. The theoretical framework presented here can be useful for the understanding of phenomena observed in magnetic glassy systems that have spin clusters as building blocks instead of individual spins. In particular, we suggest that our results can help to explain the magnetic behaviour of the rare earth TbIn0.99Mn0.01O3, which has been recently proposed to be composed of antiferromagnetic clusters, presenting a field-induced increase of the freezing temperature.
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Affiliation(s)
- M Schmidt
- Departamento de Física, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil
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9
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Jain P, Bansal D, Sharma G, Bhattacharya A, Ingale B, Delaire O, Chatterjee R. Observation of low temperature metastable states in complex CaMn 7O 12. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:075801. [PMID: 29350202 DOI: 10.1088/1361-648x/aaa525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The low temperature magnetic behaviour of the multiferroic quadruple perovskite CaMn7O12 is investigated. The magneto-caloric effect in this material is presented for the first time. Along with the established magnetic transitions, T N1 ~ 90 K and T N2 ~ 45 K, an anomaly at 20 K is observed in our dc magnetization, ac susceptibility and dielectric measurements; below which, an inverse magnetocaloric effect is also observed in our -ΔS M (T) plots. The neutron scattering measurements show minimal change between 10 K and 30 K in static correlations, but a clear change in energy and linewidth of the magnetic excitations is evident. The results suggest that only dynamic correlations change across T M ~ 20 K. The existence of multiple magnetic interactions below 45 K, with significant coupling between them, is demonstrated using an Arrott plot analysis of our magnetic data. Compatible conclusions are drawn from magnetocaloric plots. The peak change in isothermal magnetic entropy (-ΔS M) is 1.3 JK-1 kg-1 and the value of refrigeration capacity in CaMn7O12 is 34.5 J · kg-1 at 7 T.
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Affiliation(s)
- Parul Jain
- Magnetics and Advanced Ceramics Laboratory, Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India
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10
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Kumar M, Banerjee V, Puri S. Random field Ising model in a uniform magnetic field: Ground states, pinned clusters and scaling laws. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:96. [PMID: 29110112 DOI: 10.1140/epje/i2017-11584-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2017] [Accepted: 10/23/2017] [Indexed: 06/07/2023]
Abstract
In this paper, we study the random field Ising model (RFIM) in an external magnetic field h . A computationally efficient graph-cut method is used to study ground state (GS) morphologies in this system for three different disorder types: Gaussian, uniform and bimodal. We obtain the critical properties of this system and find that they are independent of the disorder type. We also study GS morphologies via pinned-cluster distributions, which are scale-free at criticality. The spin-spin correlation functions (and structure factors) are characterized by a roughness exponent [Formula: see text]. The corresponding scaling function is universal for all disorder types and independent of h.
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Affiliation(s)
- Manoj Kumar
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology, 110016, Hauz Khas, New Delhi, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India.
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11
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Fytas NG, Martín-Mayor V. Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions. Phys Rev E 2016; 93:063308. [PMID: 27415388 DOI: 10.1103/physreve.93.063308] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Indexed: 06/06/2023]
Abstract
It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.
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Affiliation(s)
- Nikolaos G Fytas
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Víctor Martín-Mayor
- Departamento de Física Teórica I, Universidad Complutense, E-28040 Madrid, Spain and Instituto de Biocomputación and Física de Sistemas Complejos (BIFI), E-50009 Zaragoza, Spain
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12
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Salmon ODR, Nobre FD. Anisotropic four-state clock model in the presence of random fields. Phys Rev E 2016; 93:022125. [PMID: 26986306 DOI: 10.1103/physreve.93.022125] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2015] [Indexed: 11/07/2022]
Abstract
A four-state clock ferromagnetic model is studied in the presence of different configurations of anisotropies and random fields. The model is considered in the limit of infinite-range interactions, for which the mean-field approach becomes exact. Both representations of Cartesian spin components and two Ising variables are used, in terms of which the physical properties and phase diagrams are discussed. The random fields follow bimodal probability distributions and the richest criticality is found when the fields, applied in the two Ising systems, are not correlated. The phase diagrams present new interesting topologies, with a wide variety of critical points, which are expected to be useful in describing different complex phenomena.
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Affiliation(s)
| | - Fernando D Nobre
- Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro - RJ, Brazil
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13
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Bupathy A, Banerjee V, Puri S. Random-field Ising model on isometric lattices: Ground states and non-Porod scattering. Phys Rev E 2016; 93:012104. [PMID: 26871021 DOI: 10.1103/physreve.93.012104] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2015] [Indexed: 11/07/2022]
Abstract
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δ_{c} at zero temperature with high accuracy. For the SC lattice, our estimate (Δ_{c}=2.278±0.002) is consistent with earlier reports. For the BCC and FCC lattices, Δ_{c}=3.316±0.002 and 5.160±0.002, respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α=0.5±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy E_{i}(L) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
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Affiliation(s)
- Arunkumar Bupathy
- Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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14
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Shrivastav GP, Banerjee V, Puri S. Non-Porod behavior in systems with rough morphologies. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:98. [PMID: 25348663 DOI: 10.1140/epje/i2014-14098-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2014] [Revised: 09/24/2014] [Accepted: 10/10/2014] [Indexed: 05/28/2023]
Abstract
Many experiments yield multi-scale morphologies which are smooth on some length scales and fractal on others. Accurate statements about morphological properties, e.g., roughness exponent, fractal dimension, domain size, interfacial width, etc. are obtained from the correlation function and structure factor. In this paper, we present structure factor data for two systems: (a) droplet-in-droplet morphologies of double-phase-separating mixtures; and (b) ground-state morphologies in dilute anti-ferromagnets. An important characteristic of the scattering data is a non-Porod tail, which is associated with scattering off rough domains and interfaces.
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Affiliation(s)
- Gaurav P Shrivastav
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India
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15
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Shrivastav GP, Kumar M, Banerjee V, Puri S. Ground-state morphologies in the random-field Ising model: scaling properties and non-Porod behavior. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032140. [PMID: 25314428 DOI: 10.1103/physreve.90.032140] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2014] [Indexed: 06/04/2023]
Abstract
We use a computationally efficient graph-cut method (GCM) to obtain the ground-state morphologies (at zero temperature) of the random-field Ising model in d=2,3. The GCM enables us to obtain comprehensive numerical results on large-scale systems. We analyze the morphologies by computing correlation functions and structure factors. These quantities enable us to precisely evaluate characteristic properties, e.g., domain sizes, scaling functions, roughness exponents, fractal dimensions, etc.
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Affiliation(s)
- Gaurav P Shrivastav
- Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India and School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Manoj Kumar
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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16
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Herlitschke M, Tchougréeff AL, Soudackov AV, Klobes B, Stork L, Dronskowski R, Hermann RP. Magnetism and lattice dynamics of FeNCN compared to FeO. NEW J CHEM 2014. [DOI: 10.1039/c4nj00097h] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The Mössbauer spectra of FeNCN at 6 and 296 K reveal that, in contrast to the usual behaviour, the hyperfine magnetic field is reduced upon cooling.
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Affiliation(s)
- M. Herlitschke
- Jülich Centre for Neutron Science JCNS and Peter Grünberg Institute PGI
- JARA-FIT
- Forschungszentrum Jülich GmbH
- D-52425 Jülich, Germany
- Faculté des Sciences
| | - A. L. Tchougréeff
- Chair of Solid-State and Quantum Chemistry
- RWTH Aachen University
- D-52056 Aachen, Germany
- Independent University of Moscow
- Moscow Center for Continuous Mathematical Education
| | - A. V. Soudackov
- Department of Chemistry
- University of Illinois at Urbana-Champaign
- Urbana, USA
| | - B. Klobes
- Jülich Centre for Neutron Science JCNS and Peter Grünberg Institute PGI
- JARA-FIT
- Forschungszentrum Jülich GmbH
- D-52425 Jülich, Germany
| | - L. Stork
- Chair of Solid-State and Quantum Chemistry
- RWTH Aachen University
- D-52056 Aachen, Germany
| | - R. Dronskowski
- Chair of Solid-State and Quantum Chemistry
- RWTH Aachen University
- D-52056 Aachen, Germany
| | - R. P. Hermann
- Jülich Centre for Neutron Science JCNS and Peter Grünberg Institute PGI
- JARA-FIT
- Forschungszentrum Jülich GmbH
- D-52425 Jülich, Germany
- Faculté des Sciences
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17
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Andresen JC, Thomas CK, Katzgraber HG, Schechter M. Novel disordering mechanism in ferromagnetic systems with competing interactions. PHYSICAL REVIEW LETTERS 2013; 111:177202. [PMID: 24206516 DOI: 10.1103/physrevlett.111.177202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2012] [Revised: 07/11/2013] [Indexed: 06/02/2023]
Abstract
Ferromagnetic Ising systems with competing interactions are considered in the presence of a random field. We find that in three space dimensions the ferromagnetic phase is disordered by a random field which is considerably smaller than the typical interaction strength between the spins. This is the result of a novel disordering mechanism triggered by an underlying spin-glass phase. Calculations for the specific case of the long-range dipolar LiHo(x)Y(1-x)F(4) compound suggest that the above mechanism is responsible for the peculiar dependence of the critical temperature on the strength of the random field and the broadening of the susceptibility peaks as temperature is decreased, as found in recent experiments by Silevitch et al.. [Nature (London) 448, 567 (2007)]. Our results thus emphasize the need to go beyond the standard Imry-Ma argument when studying general random-field systems.
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18
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Fedorenko AA. Random-field and random-anisotropy O(N) spin systems with a free surface. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:021131. [PMID: 23005746 DOI: 10.1103/physreve.86.021131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2012] [Revised: 07/12/2012] [Indexed: 06/01/2023]
Abstract
We study the surface scaling behavior of a semi-infinite d-dimensional O(N) spin system in the presence of a quenched random field and random anisotropy disorders. It is known that above the lower critical dimension d(LC) = 4 the infinite models undergo a paramagnetic-ferromagnetic transition for N > N(c) (N(c) = 2.835 for the random field and N(c) =9.441 for random anisotropy). For N < N(c) and d < d(LC) there exists a quasi-long-range-order phase with a zero order parameter and a power-law decay of spin correlations. Using a functional renormalization group, we derive the surface scaling laws that describe the ordinary surface transition for d > d(LC) and the long-range behavior of spin correlations near the surface in the quasi-long-range-order phase for d < d(LC). The corresponding surface exponents are calculated to one-loop order. The obtained results can be applied to the surface scaling of periodic elastic systems in disordered media, amorphous magnets, and (3)He-A in aerogel.
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Affiliation(s)
- Andrei A Fedorenko
- Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, Unité Mixte de Recherche No 5672 Associée au Centre National de la Recherche Scientifique, 46 Allée d'Italie, 69007 Lyon, France
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19
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Yüksel Y, Vatansever E, Akıncı U, Polat H. Nonequilibrium phase transitions and stationary-state solutions of a three-dimensional random-field Ising model under a time-dependent periodic external field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051123. [PMID: 23004719 DOI: 10.1103/physreve.85.051123] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2012] [Indexed: 06/01/2023]
Abstract
Nonequilibrium behavior and dynamic phase-transition properties of a kinetic Ising model under the influence of periodically oscillating random fields have been analyzed within the framework of effective-field theory based on a decoupling approximation. A dynamic equation of motion has been solved for a simple-cubic lattice (q=6) by utilizing a Glauber-type stochastic process. Amplitude of the sinusoidally oscillating magnetic field is randomly distributed on the lattice sites according to bimodal and trimodal distribution functions. For a bimodal type of amplitude distribution, it is found in the high-frequency regime that the dynamic phase diagrams of the system in the temperature versus field amplitude plane resemble the corresponding phase diagrams of the pure kinetic Ising model. Our numerical results indicate that for a bimodal distribution, both in the low- and high-frequency regimes, the dynamic phase diagrams always exhibit a coexistence region in which the stationary state (ferro or para) of the system is completely dependent on the initial conditions, whereas for a trimodal distribution, the coexistence region disappears depending on the values of the system parameters.
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Affiliation(s)
- Yusuf Yüksel
- Department of Physics, Dokuz Eylül University, TR-35160 Izmir, Turkey
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20
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Gingras MJP, Henelius P. Collective Phenomena in the LiHoxY1−xF4Quantum Ising Magnet: Recent Progress and Open Questions. ACTA ACUST UNITED AC 2011. [DOI: 10.1088/1742-6596/320/1/012001] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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21
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Akıncı U, Yüksel Y, Polat H. Effective-field-theory analysis of the three-dimensional random-field Ising model on isometric lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061103. [PMID: 21797298 DOI: 10.1103/physreve.83.061103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2011] [Indexed: 05/31/2023]
Abstract
An Ising model with quenched random magnetic fields is examined for single-Gaussian, bimodal, and double-Gaussian random-field distributions by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. Random-field distribution shape dependencies of the phase diagrams and magnetization curves are investigated for simple cubic, body-centered-cubic, and face-centered-cubic lattices. The conditions for the occurrence of reentrant behavior and tricritical points on the system are also discussed in detail.
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Affiliation(s)
- Umit Akıncı
- Department of Physics, Dokuz Eylül University, Izmir, Turkey
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22
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Efraim H, Peleg Y, Kanter I, Shental O, Kabashima Y. Statistical-mechanics approach to wide-band digital communication. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:060101. [PMID: 21230631 DOI: 10.1103/physreve.82.060101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2010] [Indexed: 05/30/2023]
Abstract
The emerging popular scheme of fourth generation wireless communication, orthogonal frequency-division multiplexing, is mapped onto a variant of a random field Ising Hamiltonian and results in an efficient physical intercarrier interference (ICI) cancellation decoding scheme. This scheme is based on Monte Carlo (MC) dynamics at zero temperature as well as at the Nishimori temperature and demonstrates improved bit error rate (BER) and robust convergence time compared to the state of the art ICI cancellation decoding scheme. An optimal BER performance is achieved with MC dynamics at the Nishimori temperature but with a substantial computational cost overhead. The suggested ICI cancellation scheme also supports the transmission of biased signals.
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Affiliation(s)
- Hadar Efraim
- Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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23
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Vink RLC, Fischer T, Binder K. Finite-size scaling in Ising-like systems with quenched random fields: evidence of hyperscaling violation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051134. [PMID: 21230464 DOI: 10.1103/physreve.82.051134] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2010] [Indexed: 05/30/2023]
Abstract
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced with a modified hyperscaling relation. As a result, standard formulations of finite-size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free-energy cost ΔF of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, ΔF∝L(θ), with θ as the violation of hyperscaling critical exponent and L as the linear extension of the system. This modified behavior facilitates a number of numerical approaches that can be used to locate critical points in random field systems from finite-size simulation data. We test and confirm the approaches on two random field systems in three dimensions, namely, the random field Ising model and the demixing transition in the Widom-Rowlinson fluid with quenched obstacles.
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Affiliation(s)
- R L C Vink
- Institute of Theoretical Physics, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
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24
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Stock C, Jonas S, Broholm C, Nakatsuji S, Nambu Y, Onuma K, Maeno Y, Chung JH. Neutron-scattering measurement of incommensurate short-range order in single crystals of the S=1 triangular antiferromagnet NiGa(2)S(4). PHYSICAL REVIEW LETTERS 2010; 105:037402. [PMID: 20867806 DOI: 10.1103/physrevlett.105.037402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2009] [Revised: 02/11/2010] [Indexed: 05/29/2023]
Abstract
Neutron scattering is used to investigate spin correlations in ultrapure single crystals of the S=1 triangular lattice NiGa(2)S(4). Despite a Curie-Weiss temperature of Θ(CW)=-80(2) K, static (τ>1 ns) short-range (ξ(ab)=26(3) Å) incommensurate order prevails for T>1.5 K. The incommensurate modulation Q(0)=(0.155(3),0.155(3),0), Θ(CW), and the spin-wave velocity (c=4400 m/s) can be accounted for by antiferromagnetic third-nearest-neighbor interactions J(3)=2.8(6) meV and ferromagnetic nearest-neighbor coupling J(1)=-0.35(9) J(3). Interplane correlations are limited to nearest neighbors and weakened by an in-plane field. These observations show that the short-range ordered glassy phase that has been observed in a number of highly degenerate systems can persist near the clean limit.
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Affiliation(s)
- C Stock
- ISIS Facility, Rutherford Appleton Labs, Chilton, Didcot, OX11 0QX, United Kingdom
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25
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Krzakala F, Ricci-Tersenghi F, Zdeborová L. Elusive spin-glass phase in the random field Ising model. PHYSICAL REVIEW LETTERS 2010; 104:207208. [PMID: 20867061 DOI: 10.1103/physrevlett.104.207208] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2009] [Revised: 04/07/2010] [Indexed: 05/29/2023]
Abstract
We show rigorously that the spin-glass susceptibility in the random field Ising model is always bounded by the ferromagnetic susceptibility, and therefore that no spin-glass phase can be present at equilibrium out of the ferromagnetic critical line. When the magnetization is, however, fixed to values smaller than the equilibrium value, a spin-glass phase can exist, as we show explicitly on the Bethe lattice.
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Affiliation(s)
- Florent Krzakala
- CNRS and ESPCI ParisTech, 10 rue Vauquelin, UMR 7083 Gulliver, Paris 75000 France
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26
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Crokidakis N. Nonequilibrium phase transitions and tricriticality in a three-dimensional lattice system with random-field competing kinetics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:041138. [PMID: 20481708 DOI: 10.1103/physreve.81.041138] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2009] [Revised: 02/27/2010] [Indexed: 05/29/2023]
Abstract
We study a nonequilibrium Ising model that stochastically evolves under the simultaneous operation of several spin-flip mechanisms. In other words, the local magnetic fields change sign randomly with time due to competing kinetics. This dynamics models a fast and random diffusion of disorder that takes place in dilute metallic alloys when magnetic ions diffuse. We perform Monte Carlo simulations on cubic lattices up to L=60. The system exhibits ferromagnetic and paramagnetic steady states. Our results predict first-order transitions at low temperatures and large disorder strengths, which correspond to the existence of a nonequilibrium tricritical point at finite temperature. By means of standard finite-size scaling equations, we estimate the critical exponents in the low-field region, for which our simulations uphold continuous phase transitions.
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Affiliation(s)
- Nuno Crokidakis
- Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, 24210-340 Niterói, RJ, Brazil.
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27
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Silevitch DM, Aeppli G, Rosenbaum TF. Switchable hardening of a ferromagnet at fixed temperature. Proc Natl Acad Sci U S A 2010; 107:2797-800. [PMID: 20133728 PMCID: PMC2840359 DOI: 10.1073/pnas.0910575107] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The intended use of a magnetic material, from information storage to power conversion, depends crucially on its domain structure, traditionally crafted during materials synthesis. By contrast, we show that an external magnetic field, applied transverse to the preferred magnetization of a model disordered uniaxial ferromagnet, is an isothermal regulator of domain pinning. At elevated temperatures, near the transition into the paramagnet, modest transverse fields increase the pinning, stabilize the domain structure, and harden the magnet, until a point where the field induces quantum tunneling of the domain walls and softens the magnet. At low temperatures, tunneling completely dominates the domain dynamics and provides an interpretation of the quantum phase transition in highly disordered magnets as a localization/delocalization transition for domain walls. While the energy scales of the rare earth ferromagnet studied here restrict the effects to cryogenic temperatures, the principles discovered are general and should be applicable to existing classes of highly anisotropic ferromagnets with ordering at room temperature or above.
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Affiliation(s)
- D. M. Silevitch
- The James Franck Institute and Department of Physics, The University of Chicago, 929 East 57th Street, Chicago, IL 60637 and
| | - G. Aeppli
- London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
| | - T. F. Rosenbaum
- The James Franck Institute and Department of Physics, The University of Chicago, 929 East 57th Street, Chicago, IL 60637 and
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28
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Miyashita S. Phase transition in spin systems with various types of fluctuations. PROCEEDINGS OF THE JAPAN ACADEMY. SERIES B, PHYSICAL AND BIOLOGICAL SCIENCES 2010; 86:643-66. [PMID: 20689226 PMCID: PMC3066537 DOI: 10.2183/pjab.86.643] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/04/2010] [Accepted: 05/25/2010] [Indexed: 05/29/2023]
Abstract
Various types ordering processes in systems with large fluctuation are overviewed. Generally, the so-called order-disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance. Nature of the phase transition strongly depends on the type of fluctuation which is determined by the structure of the order parameter of the system. As to the critical property of phase transitions, the concept "universality of the critical phenomena" is well established. However, we still find variety of features of ordering processes. In this article, we study effects of various mechanisms which bring large fluctuation in the system, e.g., continuous symmetry of the spin in low dimensions, contradictions among interactions (frustration), randomness of the lattice, quantum fluctuations, and a long range interaction in off-lattice systems.
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29
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Duarte Queirós SM, Crokidakis N, Soares-Pinto DO. Effect of platykurtic and leptokurtic distributions in the random-field Ising model: mean-field approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:011143. [PMID: 19658689 DOI: 10.1103/physreve.80.011143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2009] [Revised: 06/15/2009] [Indexed: 05/28/2023]
Abstract
The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose value is in accordance with a generic distribution that bears platykurtic and leptokurtic distributions depending on a single parameter tau<3 to each site. For tau<5/3, such distributions, which are basically Student-t and r distribution extended for all plausible real degrees of freedom, present a finite standard deviation, if not the distribution has got the same asymptotic power-law behavior as a alpha-stable Lévy distribution with alpha=(3-tau)/(tau-1). For every value of tau, at specific temperature and width of the distribution, the system undergoes a continuous phase transition. Strikingly, we impart the emergence of an inflexion point in the temperature-PDF width phase diagrams for distributions broader than the Cauchy-Lorentz (tau=2) which is accompanied with a divergent free energy per spin (at zero temperature).
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30
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Mulders AM, Loosvelt H, Fraile Rodríguez A, Popova E, Konishi T, Temst K, Karis O, Arvanitis D, Van Haesendonck C. On the interface magnetism of thin oxidized Co films: orbital and spin moments. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:124211. [PMID: 21817453 DOI: 10.1088/0953-8984/21/12/124211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
An x-ray magnetic circular dichroism study of a polycrystalline Co/CoO bilayer is presented. Using both the chemical specificity and surface sensitivity in the core level techniques, we find that uncompensated Co(2+) spin moments participate in the remanent ferromagnetic response of the bilayer that has oxygen nearest neighbors. These are likely located at the Co/CoO interface. As intermixing of magnetic species is not present in Co/CoO, it is concluded that the observed interface moments are due to interface roughness. Given their direction, these moments appear to not directly correlate to the exchange bias in these bilayers.
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Affiliation(s)
- A M Mulders
- Department of Physics, Uppsala University, Box 530, 751 21 Uppsala, Sweden. Department of Imaging and Applied Physics, Curtin University of Technology, Perth, WA 6845, Australia. The Bragg Institute, Australian Nuclear Science and Technology Organization, Lucas Heights, NSW 2234, Australia
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31
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Salmon OR, Crokidakis N, Nobre FD. Multicritical behavior in a random-field Ising model under a continuous-field probability distribution. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:056005. [PMID: 21817311 DOI: 10.1088/0953-8984/21/5/056005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
A random-field Ising model that is capable of exhibiting a rich variety of multicritical phenomena, as well as a smearing of such behavior, is investigated. The model consists of an infinite-range-interaction Ising ferromagnet in the presence of a triple Gaussian random magnetic field, which is defined as a superposition of three Gaussian distributions with the same width σ, centered at H = 0 and H = ± H(0), with probabilities p and (1-p)/2, respectively. Such a distribution is very general and recovers, as limiting cases, the trimodal, bimodal and Gaussian probability distributions. In particular, the special case of the random-field Ising model in the presence of a trimodal probability distribution (limit [Formula: see text]) is able to present a rather nontrivial multicritical behavior. It is argued that the triple Gaussian probability distribution is appropriate for a physical description of some diluted antiferromagnets in the presence of a uniform external field, for which the corresponding physical realization consists of an Ising ferromagnet under random fields whose distribution appears to be well represented in terms of a superposition of two parts, namely a trimodal and a continuous contribution. The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution, which is known to be stable for the present system. A rich variety of phase diagrams is presented, with one or two distinct ferromagnetic phases, continuous and first-order transition lines, tricritical, fourth-order, critical end points and many other interesting multicritical phenomena. Additionally, the present model carries the possibility of destroying such multicritical phenomena due to an increase in the randomness, i.e. increasing σ, which represents a very common feature in real systems.
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Affiliation(s)
- Octavio R Salmon
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro-RJ, Brazil
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32
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Benitez MJ, Petracic O, Salabas EL, Radu F, Tüysüz H, Schüth F, Zabel H. Evidence for core-shell magnetic behavior in antiferromagnetic Co3O4 nanowires. PHYSICAL REVIEW LETTERS 2008; 101:097206. [PMID: 18851655 DOI: 10.1103/physrevlett.101.097206] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2008] [Indexed: 05/26/2023]
Abstract
Employing magnetometry measurements, we have studied Co3O4 nanowires focusing on the core-shell behavior. We find two magnetic contributions, i.e., a regular antiferromagnetic and an additional irreversible one. The first contribution can be attributed to the antiferromagnetically ordered wire cores. The nature of the second one can be identified using thermoremanent and isothermoremanent magnetizaton curves as magnetic fingerprints of the irreversible magnetization. We conclude that the nanowire shell behaves like a two-dimensional diluted antiferromagnet in a field.
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Affiliation(s)
- M J Benitez
- Institut für Experimentalphysik/Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany.
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33
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Crokidakis N, Nobre FD. Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:041124. [PMID: 18517595 DOI: 10.1103/physreve.77.041124] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2008] [Indexed: 05/26/2023]
Abstract
The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two Gaussian distributions centered, respectively, at +H0 and -H0, presenting the same width sigma . It is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular two well-known limits, namely, the single Gaussian distribution (sigma>>H0) and the bimodal one (sigma=0) . The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution. Critical frontiers exhibiting tricritical points occur for different values of sigma , with the possibility of two tricritical points along the same critical frontier. To our knowledge, it is the first time that such a behavior is verified for a spin-glass model in the presence of a continuous-distribution random field, which represents a typical situation of a real system. The stability of the replica-symmetric solution is analyzed, and the usual Almeida-Thouless instability is verified for low temperatures. It is verified that the higher-temperature tricritical point always appears in the region of stability of the replica-symmetric solution; a condition involving the parameters H0 and sigma , for the occurrence of this tricritical point only, is obtained analytically. Some of our results are discussed in view of experimental measurements available in the literature.
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Affiliation(s)
- Nuno Crokidakis
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil.
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34
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Silevitch DM, Bitko D, Brooke J, Ghosh S, Aeppli G, Rosenbaum TF. A ferromagnet in a continuously tunable random field. Nature 2007; 448:567-70. [PMID: 17671498 DOI: 10.1038/nature06050] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2007] [Accepted: 06/19/2007] [Indexed: 11/09/2022]
Abstract
Most physical and biological systems are disordered, even though the majority of theoretical models treat disorder as a weak perturbation. One particularly simple system is a ferromagnet approaching its Curie temperature, T(C), where all of the spins associated with partially filled atomic shells acquire parallel orientation. With the addition of disorder by way of chemical substitution, the Curie point is suppressed, but no qualitatively new phenomena appear in bulk measurements as long as the disorder is truly random on the atomic scale and not so large as to eliminate ferromagnetism entirely. Here we report the discovery that a simply measured magnetic response is singular above the Curie temperature of a model, disordered magnet, and that the associated singularity grows to an anomalous divergence at T(C). The origin of the singular response is the random internal field induced by an external magnetic field transverse to the favoured direction for magnetization. The fact that ferromagnets can be studied easily and with high precision using bulk susceptibility and a large variety of imaging tools will not only advance fundamental studies of the random field problem, but also suggests a mechanism for tuning the strength of domain wall pinning, the key to applications.
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Affiliation(s)
- D M Silevitch
- The James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
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35
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Stone MB, Broholm C, Reich DH, Tchernyshyov O, Vorderwisch P, Harrison N. Quantum criticality in an organic magnet. PHYSICAL REVIEW LETTERS 2006; 96:257203. [PMID: 16907338 DOI: 10.1103/physrevlett.96.257203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2005] [Revised: 02/14/2006] [Indexed: 05/11/2023]
Abstract
Exchange interactions between S=1/2 sites in piperazinium hexachlorodicuprate produce a frustrated bilayer magnet with a singlet ground state. We have determined the field-temperature phase diagram by high field magnetization and neutron scattering experiments. There are two quantum critical points: Hc1=7.5 T separates a quantum paramagnet phase from a three dimensional, antiferromagnetically ordered state while Hc2=37 marks the onset of a fully polarized state. The ordered phase, which we describe as a magnon Bose-Einstein condensate (BEC), is embedded in a quantum critical regime with short range correlations. A low temperature anomaly in the BEC phase boundary indicates that additional low energy features of the material become important near Hc1.
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Affiliation(s)
- M B Stone
- Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennennesse 37831, USA
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De S, Shapir Y, Chimowitz EH, Kumaran V. Critical behavior in quenched random structures: Mean-field lattice-gas approach. AIChE J 2006. [DOI: 10.1002/aic.690470223] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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37
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Malakis A, Fytas NG. Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:016109. [PMID: 16486218 DOI: 10.1103/physreve.73.016109] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2004] [Revised: 11/28/2005] [Indexed: 05/06/2023]
Abstract
We apply the recently developed critical minimum-energy subspace scheme for the investigation of the random-field Ising model. We point out that this method is well suited for the study of this model. The density of states is obtained via the Wang-Landau and broad histogram methods in a unified implementation by employing the N-fold version of the Wang-Landau scheme. The random fields are obtained from a bimodal distribution (hi = +/-2), and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from L=4 to L=32. Observing the finite-size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat. The lack of self-averaging of this quantity is fully illustrated, and it is shown that this property may be related to the question mentioned above.
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Affiliation(s)
- Anastasios Malakis
- Department of Physics, Section of Solid State Physics, University of Athens, Panepistimiopolis, GR 15784 Zografos, Athens, Greece
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38
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Prozorov R, Lawrie DD, Hetel I, Fournier P, Giannetta RW. Field-dependent diamagnetic transition in magnetic superconductor Sm1.85Ce0.15CuO4-y. PHYSICAL REVIEW LETTERS 2004; 93:147001. [PMID: 15524829 DOI: 10.1103/physrevlett.93.147001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2004] [Indexed: 05/24/2023]
Abstract
The magnetic penetration depth of single crystal Sm(1.85)Ce(0.15)CuO(4-y) was measured down to 0.4 K in dc fields up to 7 kOe. For insulating Sm2CuO4, Sm3+ spins order at the Ne el temperature, T(N)=6 K, independent of the applied field. Superconducting Sm(1.85)Ce(0.15)CuO(4-y) (T(c) approximately 23 K) shows a sharp increase in diamagnetic screening below T(*)(H) which varied from 4.0 K (H=0) to 0.5 K (H=7 kOe) for a field along the c axis. If the field was aligned parallel to the conducting planes, T(*) remained unchanged. The unusual field dependence of T(*) indicates a spin-freezing transition that dramatically increases the superfluid density.
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Affiliation(s)
- R Prozorov
- Loomis Laboratory of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
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39
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Faleev SV, van Schilfgaarde M, Kotani T. All-electron self-consistent GW approximation: application to Si, MnO, and NiO. PHYSICAL REVIEW LETTERS 2004; 93:126406. [PMID: 15447292 DOI: 10.1103/physrevlett.93.126406] [Citation(s) in RCA: 100] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2003] [Indexed: 05/24/2023]
Abstract
We present a new kind of self-consistent GW approximation based on the all-electron, full-potential linear muffin-tin orbital method. By iterating the eigenfunctions of the GW Hamiltonian, self-consistency in both the charge density and the quasiparticle spectrum is achieved. We explain why this form of self-consistency should be preferred to the conventional one. Some results for Si (a representative semiconductor) are presented. Finally we consider many details in the electronic structure of the antiferromagnetic insulators MnO and NiO. Excellent agreement with experiment is shown for many properties, suggesting that a Landau quasiparticle (energy band) picture provides a reasonable description of electronic structure even in these correlated materials.
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Calabrese P, Parruccini P, Pelissetto A, Vicari E. Crossover behavior in three-dimensional dilute spin systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:036120. [PMID: 15089374 DOI: 10.1103/physreve.69.036120] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2003] [Indexed: 05/24/2023]
Abstract
We study the crossover behaviors that can be observed in the high-temperature phase of three-dimensional dilute spin systems, using a field-theoretical approach. In particular, for randomly dilute Ising systems we consider the Gaussian-to-random and the pure-Ising-to-random crossover, determining the corresponding crossover functions for the magnetic susceptibility and the correlation length. Moreover, for the physically interesting cases of dilute Ising, XY, and Heisenberg systems, we estimate several universal ratios of scaling-correction amplitudes entering the high-temperature Wegner expansion of the magnetic susceptibility, of the correlation length, and of the zero-momentum quartic couplings.
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Affiliation(s)
- Pasquale Calabrese
- Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.
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41
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van Duijn J, Gaulin BD, Lumsden MA, Castellan JP, Buyers WJL. Random fields and the partially paramagnetic state of CsCo0.83Mg0.17Br3: critical scattering study. PHYSICAL REVIEW LETTERS 2004; 92:077202. [PMID: 14995878 DOI: 10.1103/physrevlett.92.077202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2002] [Indexed: 05/24/2023]
Abstract
We have performed measurements of the critical neutron scattering on CsCo0.83Mg0.17Br3, a dilute stacked triangular lattice (STL) Ising antiferromagnet (AF). A two component line shape associated with the critical fluctuations appears at a temperature coincident with T(N1) observed in pure CsCoBr3. Such scattering is indicative of fluctuations in prototypical random field Ising model (RFIM) systems. The random field domain state arises in this case due to geometrical frustration within the STL Ising AF, which gives rise to a three sublattice Néel state, in which one sublattice is disordered. Magnetic vacancies nucleate AF domains in which the vacancies reside on the disordered sublattice thereby generating a RFIM state in the absence of an applied magnetic field.
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Affiliation(s)
- J van Duijn
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1
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42
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Papavassiliou G, Pissas M, Belesi M, Fardis M, Dolinsek J, Dimitropoulos C, Ansermet JP. Orbital domain state and finite size scaling in ferromagnetic insulating manganites. PHYSICAL REVIEW LETTERS 2003; 91:147205. [PMID: 14611553 DOI: 10.1103/physrevlett.91.147205] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2002] [Indexed: 05/24/2023]
Abstract
55Mn and 139La NMR measurements on a high quality single crystal of ferromagnetic (FM) La0.80Ca0.20MnO3 demonstrate the formation of localized Mn(3+,4+) states below 70 K, accompanied by a strong cooling-rate dependent increase of certain FM neutron Bragg peaks. (55,139)(1/T(1)) spin-lattice and (139)(1/T(2)) spin-spin relaxation rates are strongly enhanced on approaching this temperature from below, signaling a genuine phase transition at T(tr) approximately 70 K. The disappearance of the FM metallic signal by applying a weak external magnetic field, the different NMR radio-frequency enhancement of the FM metallic and insulating states, and the observed finite size scaling of T(tr) with Ca (hole) doping, as observed in powder La(1-x)CaxMnO3 samples, are suggestive of freezing into an inhomogeneous FM insulating and orbitally ordered state embodying "metallic" hole-rich walls.
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Affiliation(s)
- G Papavassiliou
- Institute of Materials Science, NCSR, Demokritos, 153 10 Aghia Paraskevi, Athens, Greece
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43
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Calabrese P, Martín-Mayor V, Pelissetto A, Vicari E. Three-dimensional randomly dilute Ising model: Monte Carlo results. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:036136. [PMID: 14524861 DOI: 10.1103/physreve.68.036136] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2003] [Indexed: 05/24/2023]
Abstract
We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices L3 with L< or =256. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining nu=0.683(3), eta=0.035(2), beta=0.3535(17), and alpha=-0.049(9), in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio R(+)(xi) that expresses the universality of the free-energy density per correlation volume. We find R(+)(xi)=0.2885(15).
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Affiliation(s)
- Pasquale Calabrese
- Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.
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Clegg PS, Stock C, Birgeneau RJ, Garland CW, Roshi A, Iannacchione GS. Effect of a quenched random field on a continuous symmetry breaking transition: nematic to smectic-A transition in octyloxycyanobiphenyl-aerosil dispersions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:021703. [PMID: 12636696 DOI: 10.1103/physreve.67.021703] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2002] [Indexed: 05/24/2023]
Abstract
High-resolution x-ray diffraction and ac-calorimetric experiments have been carried out on the liquid-crystal octyloxycyanobiphenyl in which aerosil particles are dispersed. The measurements were made over a temperature range around the bulk nematic to smectic-A transition temperature. At this transition the liquid crystal breaks translational symmetry in a single direction. The silica particles, which hydrogen bond together to form a very low density gel, provide the quenched disorder. The random gel leads to observable broadening of the x-ray reflection from the smectic layers. The structure factor is well described by modeling the effect of the aerosils as a quenched random field. Dispersed aerosils are thought to pin both the direction of the translational ordering and the position of the layers. The latter appears to have the greatest effect on the x-ray line shape. We show that the aerosil surface area, as verified by small-angle scattering, equates to the variance of the random field. Calorimetric results reveal substantial change in the specific heat peak associated with the nematic to smectic-A transition. As the concentration of aerosil increases, the specific heat peak remains sharp yet decreases in magnitude and shifts in temperature in a nonmonotonic fashion. In this regime, the critical exponent alpha becomes progressively smaller. For the samples with the largest concentrations of aerosil particles the C(p)(N-A) peak becomes highly smeared and shifts smoothly to lower temperatures.
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Affiliation(s)
- P S Clegg
- Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
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Folk R, Holovatch Y, Yavorskii T. Critical exponents of a three-dimensional weakly diluted quenched Ising model. ACTA ACUST UNITED AC 2003. [DOI: 10.3367/ufnr.0173.200302c.0175] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/01/2022]
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46
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Ye F, Zhou L, Larochelle S, Lu L, Belanger DP, Greven M, Lederman D. Order parameter criticality of the d = 3 random-field Ising antiferromagnet Fe0.85Zn0.15F2. PHYSICAL REVIEW LETTERS 2002; 89:157202. [PMID: 12366018 DOI: 10.1103/physrevlett.89.157202] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2002] [Indexed: 05/23/2023]
Abstract
The critical exponent beta=0.16+/-0.02 for the random-field Ising model order parameter is determined using extinction-free magnetic x-ray scattering for Fe0.85Zn0.15F2 in magnetic fields of 10 and 11 T. The observed value is consistent with other experimental random-field critical exponents, but disagrees sharply with Monte Carlo and exact ground state calculations on finite-sized systems.
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Affiliation(s)
- F Ye
- Department of Physics, University of California, Santa Cruz 95064, USA
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47
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Dobrin R, Meinke JH, Duxbury PM. Random-field Ising model on complete graphs and trees. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/0305-4470/35/19/101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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48
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Feldman DE. Critical exponents of the random-field O(N) model. PHYSICAL REVIEW LETTERS 2002; 88:177202. [PMID: 12005781 DOI: 10.1103/physrevlett.88.177202] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2000] [Indexed: 05/23/2023]
Abstract
The critical behavior of the random-field Ising model has long been a puzzle. Different methods predict that its critical exponents in D dimensions are the same as in the pure (D-2)-dimensional ferromagnet with the same number of the magnetization components contrary to the experiments and simulations. We calculate the exponents of the random-field O(N) model with the (4+epsilon)-expansion and obtain values different from the exponents of the pure ferromagnet in 2+epsilon dimensions. An infinite set of relevant operators missed in previous studies leads to a breakdown of the (6-epsilon)-expansion.
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Affiliation(s)
- D E Feldman
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
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49
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de Queiroz SL, Stinchcombe RB. Correlation functions, free energies, and magnetizations in the two-dimensional random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:036117. [PMID: 11580404 DOI: 10.1103/physreve.64.036117] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2001] [Indexed: 05/23/2023]
Abstract
Transfer-matrix methods are used to calculate spin-spin correlation functions (G), Helmholtz free energies (f) and magnetizations (m) in the two-dimensional random-field Ising model close to the zero-field bulk critical temperature T(c 0), on long strips of width L=3-18 sites, for binary field distributions. Analysis of the probability distributions of G for varying spin-spin distances R shows that describing the decay of their averaged values by effective correlation lengths is a valid procedure only for not very large R. Connections between field and correlation function distributions at high temperatures are established, yielding approximate analytical expressions for the latter, which are used for computation of the corresponding structure factor. It is shown that, for fixed R/L, the fractional widths of correlation-function distributions saturate asymptotically with L-2.2. Considering an added uniform applied field h, a connection between f(h), m(h), the Gibbs free energy g(m) and the distribution function for the uniform magnetization in a zero uniform field, P0(m), is derived and first illustrated for pure systems, and then applied for nonzero random field. From finite-size scaling and crossover arguments, coupled with numerical data, it is found that the width of P0(m) varies against (nonvanishing, but small) random-field intensity H0 as H(-3/7)(0).
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Affiliation(s)
- S L de Queiroz
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro RJ, Brazil.
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50
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Duxbury PM, Meinke JH. Ground state nonuniversality in the random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:036112. [PMID: 11580399 DOI: 10.1103/physreve.64.036112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2001] [Indexed: 05/23/2023]
Abstract
Two attractive and often used ideas, namely, universality and the concept of a zero-temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are nonuniversal. However, we also show that at finite temperature the thermal order-parameter exponent 1/2 is restored so that temperature is a relevant variable. Broader implications of these results are discussed.
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Affiliation(s)
- P M Duxbury
- Department of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University, East Lansing, Michigan 48824, USA
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