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Nyckees S, Rufino A, Mila F, Colbois J. Critical line of the triangular Ising antiferromagnet in a field from a C_{3}-symmetric corner transfer matrix algorithm. Phys Rev E 2023; 108:064132. [PMID: 38243525 DOI: 10.1103/physreve.108.064132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Accepted: 11/20/2023] [Indexed: 01/21/2024]
Abstract
The corner transfer matrix renormalization group (CTMRG) algorithm has been extensively used to investigate both classical and quantum two-dimensional (2D) lattice models. The convergence of the algorithm can strongly vary from model to model depending on the underlying geometry and symmetries, and the presence of algebraic correlations. An important factor in the convergence of the algorithm is the lattice symmetry, which can be broken due to the necessity of mapping the problem onto the square lattice. We propose a variant of the CTMRG algorithm, designed for models with C_{3}-symmetry, which we apply to the conceptually simple yet numerically challenging problem of the triangular lattice Ising antiferromagnet in a field, at zero and low temperatures. We study how the finite-temperature three-state Potts critical line in this model approaches the ground-state Kosterlitz-Thouless transition driven by a reduced field (h/T). In this particular instance, we show that the C_{3}-symmetric CTMRG leads to much more precise results than both existing results from exact diagonalization of transfer matrices and Monte Carlo.
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Affiliation(s)
- Samuel Nyckees
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Afonso Rufino
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Frédéric Mila
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jeanne Colbois
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
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2
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Yoshiyama K, Hukushima K. Higher-order tensor renormalization group study of the J_{1}-J_{2} Ising model on a square lattice. Phys Rev E 2023; 108:054124. [PMID: 38115502 DOI: 10.1103/physreve.108.054124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 10/09/2023] [Indexed: 12/21/2023]
Abstract
Phase transitions of the J_{1}-J_{2} Ising model on a square lattice are studied using the higher-order tensor renormalization group (HOTRG) method. This system involves a competition between the ferromagnetic interaction J_{1} and antiferromagnetic interaction J_{2}, and in previous studies, weak first-order and second-order transitions were observed near the ratio g=J_{2}/|J_{1}|=1/2. It has also been suggested that the universality class of the second-order phase transition connected to the first-order transition line for g>1/2 belongs to the Ashkin-Teller class, which is characterized by a continuously varying critical exponent with g, as predicted by field-theoretical and other studies. Our results, based on the HOTRG calculations for significantly larger sizes, indicate that the region of the first-order transition is marginally narrower than that in previous studies. Furthermore, it is suggested that the region where the critical exponent changes does not necessarily coincide with the Ashkin-Teller region.
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Affiliation(s)
- Kota Yoshiyama
- Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Koji Hukushima
- Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
- Komaba Institute for Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
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3
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Syzranov SV, Ramirez AP. Eminuscent phase in frustrated magnets: a challenge to quantum spin liquids. Nat Commun 2022; 13:2993. [PMID: 35637214 PMCID: PMC9151641 DOI: 10.1038/s41467-022-30739-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 05/16/2022] [Indexed: 12/04/2022] Open
Abstract
A geometrically frustrated (GF) magnet consists of localised magnetic moments, spins, whose orientation cannot be arranged to simultaneously minimise their interaction energies. Such materials may host novel fascinating phases of matter, such as fluid-like states called quantum spin-liquids. GF magnets have, like all solid-state systems, randomly located impurities whose magnetic moments may “freeze” at low temperatures, making the system enter a spin-glass state. We analyse the available data for spin-glass transitions in GF materials and find a surprising trend: the glass-transition temperature grows with decreasing impurity concentration and reaches a finite value in the impurity-free limit at a previously unidentified, “hidden”, energy scale. We propose a scenario in which the interplay of interactions and entropy leads to a crossover in the permeability of the medium that assists glass freezing at low temperatures. This low-temperature, “eminuscent”, phase may obscure or even destroy the widely-sought spin-liquid states in rather clean systems. A spin-glass forms in frustrated magnetic systems when at low temperatures impurity sites “freeze” into a random spin configuration. Here, by looking back at previous experimental results, Syzranov and Ramirez show that the glass-transition temperature grows with decreasing impurity concentration.
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4
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Erba V, Pastore M, Rotondo P. Self-Induced Glassy Phase in Multimodal Cavity Quantum Electrodynamics. PHYSICAL REVIEW LETTERS 2021; 126:183601. [PMID: 34018775 DOI: 10.1103/physrevlett.126.183601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 04/05/2021] [Indexed: 06/12/2023]
Abstract
We provide strong evidence that the effective spin-spin interaction in a multimodal confocal optical cavity gives rise to a self-induced glassy phase, which emerges exclusively from the peculiar Euclidean correlations and is not related to the presence of disorder as in standard spin glasses. As recently shown, this spin-spin effective interaction is both nonlocal and nontranslational invariant, and randomness in the atoms' positions produces a spin glass phase. Here we consider the simplest feasible disorder-free setting, where atoms form a one-dimensional regular chain and we study the thermodynamics of the resulting effective Ising model. We present extensive results showing that the system has a low-temperature glassy phase. The model depends on the adimensional parameter α=(a/w_{0})^{2}, a being a lattice spacing and w_{0} an interaction length scale. Notably, for rational values of α=p/q, the number of metastable states at low temperature grows exponentially with q and the problem of finding the ground state rapidly becomes computationally intractable, suggesting that the system develops high-energy barriers and ergodicity breaking occurs.
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Affiliation(s)
- V Erba
- Dipartimento di Fisica dell' Università degli Studi di Milano, via Celoria 16, 20100 Milano, Italy
- Istituto Nazionale di Fisica Nucleare, sezione di Milano, via Celoria 16, 20100 Milano, Italy
| | - M Pastore
- Dipartimento di Fisica dell' Università degli Studi di Milano, via Celoria 16, 20100 Milano, Italy
- Istituto Nazionale di Fisica Nucleare, sezione di Milano, via Celoria 16, 20100 Milano, Italy
- Universit Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
| | - P Rotondo
- Dipartimento di Fisica dell' Università degli Studi di Milano, via Celoria 16, 20100 Milano, Italy
- Istituto Nazionale di Fisica Nucleare, sezione di Milano, via Celoria 16, 20100 Milano, Italy
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5
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Kuśmierz Ł, Toyoizumi T. Robust random search with scale-free stochastic resetting. Phys Rev E 2019; 100:032110. [PMID: 31639919 DOI: 10.1103/physreve.100.032110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2018] [Indexed: 06/10/2023]
Abstract
A new model of search based on stochastic resetting is introduced, wherein rate of resets depends explicitly on time elapsed since the beginning of the process. It is shown that rate inversely proportional to time leads to paradoxical diffusion which mixes self-similarity and linear growth of the mean-square displacement with nonlocality and non-Gaussian propagator. It is argued that such resetting protocol offers a general and efficient search-boosting method that does not need to be optimized with respect to the scale of the underlying search problem (e.g., distance to the goal) and is not very sensitive to other search parameters. Both subdiffusive and superdiffusive regimes of the mean-squared displacement scaling are demonstrated with more general rate functions.
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Affiliation(s)
- Łukasz Kuśmierz
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Taro Toyoizumi
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
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6
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Diep HT. Phase Transition in Frustrated Magnetic Thin Film-Physics at Phase Boundaries. ENTROPY 2019; 21:e21020175. [PMID: 33266891 PMCID: PMC7514657 DOI: 10.3390/e21020175] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2018] [Revised: 02/03/2019] [Accepted: 02/10/2019] [Indexed: 12/25/2022]
Abstract
In this review, we outline some principal theoretical knowledge of the properties of frustrated spin systems and magnetic thin films. The two points we would like to emphasize: (i) the physics in low dimensions where exact solutions can be obtained; (ii) the physics at phase boundaries where interesting phenomena can occur due to competing interactions of the two phases around the boundary. This competition causes a frustration. We will concentrate our attention on magnetic thin films and phenomena occurring near the boundary of two phases of different symmetries. Two-dimensional (2D) systems are in fact the limiting case of thin films with a monolayer. Naturally, we will treat this case at the beginning. We begin by defining the frustration and giving examples of frustrated 2D Ising systems that we can exactly solve by transforming them into vertex models. We will show that these simple systems already contain most of the striking features of frustrated systems such as the high degeneracy of the ground state (GS), many phases in the GS phase diagram in the space of interaction parameters, the reentrance occurring near the boundaries of these phases, the disorder lines in the paramagnetic phase, and the partial disorder coexisting with the order at equilibrium. Thin films are then presented with different aspects: surface elementary excitations (surface spin waves), surface phase transition, and criticality. Several examples are shown and discussed. New results on skyrmions in thin films and superlattices are also displayed. By the examples presented in this review we show that the frustration when combined with the surface effect in low dimensions gives rise to striking phenomena observed in particular near the phase boundaries.
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Affiliation(s)
- Hung T Diep
- Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 80892, Avenue Adolphe Chauvin, CEDEX, 95302 Cergy-Pontoise, France
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7
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Volovik GE, Rysti J, Mäkinen JT, Eltsov VB. Spin, Orbital, Weyl and Other Glasses in Topological Superfluids. JOURNAL OF LOW TEMPERATURE PHYSICS 2018; 196:82-101. [PMID: 31274926 PMCID: PMC6570685 DOI: 10.1007/s10909-018-02132-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/23/2018] [Accepted: 12/15/2018] [Indexed: 06/09/2023]
Abstract
One of the most spectacular discoveries made in superfluid3 He confined in a nanostructured material like aerogel or nafen was the observation of the destruction of the long-range orientational order by a weak random anisotropy. The quenched random anisotropy provided by the confining material strands produces several different glass states resolved in NMR experiments in the chiral superfluid3 He-A and in the time-reversal-invariant polar phase. The smooth textures of spin and orbital order parameters in these glasses can be characterized in terms of the randomly distributed topological charges, which describe skyrmions, spin vortices and hopfions. In addition, in these skyrmion glasses the momentum-space topological invariants are randomly distributed in space. The Chern mosaic, Weyl glass, torsion glass and other exotic topological states are examples of close connections between the real-space and momentum-space topologies in superfluid3 He phases in aerogel.
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Affiliation(s)
- G. E. Volovik
- Department of Applied Physics, Aalto University, P.O. Box 15100, 00076 Aalto, Finland
- Landau Institute for Theoretical Physics, Acad. Semyonov Av., 1a, Chernogolovka, Russia 142432
| | - J. Rysti
- Department of Applied Physics, Aalto University, P.O. Box 15100, 00076 Aalto, Finland
| | - J. T. Mäkinen
- Department of Applied Physics, Aalto University, P.O. Box 15100, 00076 Aalto, Finland
| | - V. B. Eltsov
- Department of Applied Physics, Aalto University, P.O. Box 15100, 00076 Aalto, Finland
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8
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Hamze F, Jacob DC, Ochoa AJ, Perera D, Wang W, Katzgraber HG. From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems. Phys Rev E 2018; 97:043303. [PMID: 29758754 DOI: 10.1103/physreve.97.043303] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2017] [Indexed: 11/07/2022]
Abstract
We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model defined on a cubic lattice, where subproblems, whose couplers are restricted to the two values {-1,+1}, are specified on unit cubes and are parametrized by their local degeneracy. The construction is shown to be equivalent to a type of three-dimensional constraint-satisfaction problem known as the tiling puzzle. By varying the proportions of subproblem types, the Hamiltonian can span a dramatic range of typical computational complexity, from fairly easy to many orders of magnitude more difficult than prototypical bimodal and Gaussian spin glasses in three space dimensions. We corroborate this behavior via experiments with different algorithms and discuss generalizations and extensions to different types of graphs.
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Affiliation(s)
- Firas Hamze
- D-Wave Systems, Inc., 3033 Beta Avenue, Burnaby, British Columbia, Canada V5G 4M9
| | - Darryl C Jacob
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
| | - Andrew J Ochoa
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
| | - Dilina Perera
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
| | - Wenlong Wang
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
| | - Helmut G Katzgraber
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.,1QB Information Technologies, Vancouver, British Columbia, Canada V6B 4W4.,Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
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9
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Bobák A, Jurčišinová E, Jurčišin M, Žukovič M. Frustrated spin-1/2 Ising antiferromagnet on a square lattice in a transverse field. Phys Rev E 2018; 97:022124. [PMID: 29548082 DOI: 10.1103/physreve.97.022124] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Indexed: 11/07/2022]
Abstract
We investigate the phase transitions and tricritical behaviors of the frustrated Ising antiferromagnet with first- (J_{1}<0) and second- (J_{2}<0) nearest-neighbor interactions in a transverse field Ω on the square lattice using an effective-field theory with correlations based on a single-spin approximation. We have proposed a functional for the free energy to obtain the phase diagram in the T-R (R=J_{2}/|J_{1}|) or T-Ω planes. It is shown that due to the transverse field the phase transition between ordered and disordered phases changes in the tricritical point (TCP) from the second order to the first order. The longitudinal and transverse magnetizations are also studied for selected values of R and Ω. In particular, the variation of TCP at the ground state in the three-dimensional space is constructed. For some special cases, values of the critical temperature and the critical transverse field have been determined analytically.
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Affiliation(s)
- A Bobák
- Department of Theoretical Physics and Astrophysics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 041 54 Košice, Slovak Republic
| | - E Jurčišinová
- Institute of Experimental Physics, SAS, Watsonova 47, 040 01 Košice, Slovak Republic
| | - M Jurčišin
- Department of Theoretical Physics and Astrophysics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 041 54 Košice, Slovak Republic.,Institute of Experimental Physics, SAS, Watsonova 47, 040 01 Košice, Slovak Republic
| | - M Žukovič
- Department of Theoretical Physics and Astrophysics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 041 54 Košice, Slovak Republic
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10
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Wang L. Exploring cluster Monte Carlo updates with Boltzmann machines. Phys Rev E 2017; 96:051301. [PMID: 29347705 DOI: 10.1103/physreve.96.051301] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2017] [Indexed: 06/07/2023]
Abstract
Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.
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Affiliation(s)
- Lei Wang
- Beijing National Lab for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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11
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Lundow PH, Campbell IA. Ising spin glasses in two dimensions: Universality and nonuniversality. Phys Rev E 2017; 95:042107. [PMID: 28505857 DOI: 10.1103/physreve.95.042107] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2017] [Indexed: 11/07/2022]
Abstract
Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising spin glass (ISG) models in two dimensions [Lundow and Campbell, Phys. Rev. E 93, 022119 (2016)1539-375510.1103/PhysRevE.93.022119]. Here we further analyze the bimodal and Gaussian data together with data on two other continuous interaction distribution two-dimensional ISG models, the uniform and the Laplacian models, and three other discrete interaction distribution models, a diluted bimodal model, an "antidiluted" model, and a more exotic symmetric Poisson model. Comparisons between the three continuous distribution models show that not only do they share the same exponent η≡0 but that to within the present numerical precision they share the same critical exponent ν also, and so lie in a single universality class. On the other hand the critical exponents of the four discrete distribution models are not the same as those of the continuous distributions, and the present data strongly indicate that they differ from one discrete distribution model to another. This is evidence that discrete distribution ISG models in two dimensions have nonzero values of the critical exponent η and do not lie in a single universality class.
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Affiliation(s)
- P H Lundow
- Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden
| | - I A Campbell
- Laboratoire Charles Coulomb, Université Montpellier II, 34095 Montpellier, France
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12
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Thygesen PMM, Paddison JAM, Zhang R, Beyer KA, Chapman KW, Playford HY, Tucker MG, Keen DA, Hayward MA, Goodwin AL. Orbital Dimer Model for the Spin-Glass State in Y_{2}Mo_{2}O_{7}. PHYSICAL REVIEW LETTERS 2017; 118:067201. [PMID: 28234510 DOI: 10.1103/physrevlett.118.067201] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2016] [Indexed: 06/06/2023]
Abstract
The formation of a spin glass generally requires that magnetic exchange interactions are both frustrated and disordered. Consequently, the origin of spin-glass behavior in Y_{2}Mo_{2}O_{7}-in which magnetic Mo^{4+} ions occupy a frustrated pyrochlore lattice with minimal compositional disorder-has been a longstanding question. Here, we use neutron and x-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously reported PDF, extended x-ray-absorption fine structure spectroscopy, and NMR studies, and provides a new and physical explanation of the exchange disorder responsible for spin-glass formation. We show that Mo^{4+} ions displace according to a local "two-in-two-out" rule on each Mo_{4} tetrahedron, driven by orbital dimerization of Jahn-Teller active Mo^{4+} ions. Long-range orbital order is prevented by the macroscopic degeneracy of dimer coverings permitted by the pyrochlore lattice. Cooperative O^{2-} displacements yield a distribution of Mo-O-Mo angles, which in turn introduces disorder into magnetic interactions. Our study demonstrates experimentally how frustration of atomic displacements can assume the role of compositional disorder in driving a spin-glass transition.
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Affiliation(s)
- Peter M M Thygesen
- Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QR, United Kingdom
| | - Joseph A M Paddison
- Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QR, United Kingdom
- ISIS Facility, Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire OX11 0QX, United Kingdom
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332-0430, USA
| | - Ronghuan Zhang
- Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QR, United Kingdom
| | - Kevin A Beyer
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Karena W Chapman
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Helen Y Playford
- ISIS Facility, Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire OX11 0QX, United Kingdom
| | - Matthew G Tucker
- ISIS Facility, Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire OX11 0QX, United Kingdom
- Diamond Light Source, Chilton, Oxfordshire OX11 0DE, United Kingdom
- Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - David A Keen
- ISIS Facility, Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire OX11 0QX, United Kingdom
| | - Michael A Hayward
- Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QR, United Kingdom
| | - Andrew L Goodwin
- Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QR, United Kingdom
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13
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Critical exponents and scaling invariance in the absence of a critical point. Nat Commun 2016; 7:13611. [PMID: 27917865 PMCID: PMC5150222 DOI: 10.1038/ncomms13611] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2016] [Accepted: 10/18/2016] [Indexed: 11/08/2022] Open
Abstract
The paramagnetic-to-ferromagnetic phase transition is classified as a critical phenomenon due to the power-law behaviour shown by thermodynamic observables when the Curie point is approached. Here we report the observation of such a behaviour over extraordinarily many decades of suitable scaling variables in ultrathin Fe films, for certain ranges of temperature T and applied field B. This despite the fact that the underlying critical point is practically unreachable because protected by a phase with a modulated domain structure, induced by the dipole–dipole interaction. The modulated structure has a well-defined spatial period and is realized in a portion of the (T, B) plane that extends above the putative critical temperature, where thermodynamic quantities do not display any singularity. Our results imply that scaling behaviour of macroscopic observables is compatible with an avoided critical point. Thermodynamic observables develop power laws and singularities when approaching the Curie point of a ferromagnetic phase transition. Here, Saratz et al. demonstrate that topological excitations (that is, magnetic domains in Fe/Cu(100) films that even persist above the Curie point) remove those singularities compatibly with an avoided critical point.
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14
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Crystal Structure and Spin Frustration Behavior of an Oxo-centered Trinuclear Chromium(III) Complex. J CHIN CHEM SOC-TAIP 2016. [DOI: 10.1002/jccs.201600706] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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15
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Abstract
Since the discovery of spin glasses in dilute magnetic systems, their study has been largely focused on understanding randomness and defects as the driving mechanism. The same paradigm has also been applied to explain glassy states found in dense frustrated systems. Recently, however, it has been theoretically suggested that different mechanisms, such as quantum fluctuations and topological features, may induce glassy states in defect-free spin systems, far from the conventional dilute limit. Here we report experimental evidence for existence of a glassy state, which we call a spin jam, in the vicinity of the clean limit of a frustrated magnet, which is insensitive to a low concentration of defects. We have studied the effect of impurities on SrCr9pGa12-9pO19 [SCGO(p)], a highly frustrated magnet, in which the magnetic Cr(3+) (s = 3/2) ions form a quasi-2D triangular system of bipyramids. Our experimental data show that as the nonmagnetic Ga(3+) impurity concentration is changed, there are two distinct phases of glassiness: an exotic glassy state, which we call a spin jam, for the high magnetic concentration region (p > 0.8) and a cluster spin glass for lower magnetic concentration (p < 0.8). This observation indicates that a spin jam is a unique vantage point from which the class of glassy states of dense frustrated magnets can be understood.
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16
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Electronic polymers and soft-matter-like broken symmetries in underdoped cuprates. Nat Commun 2015; 6:7691. [PMID: 26144868 PMCID: PMC4506492 DOI: 10.1038/ncomms8691] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2014] [Accepted: 05/29/2015] [Indexed: 11/12/2022] Open
Abstract
Empirical evidence in heavy fermion, pnictide and other systems suggests that unconventional superconductivity appears associated to some form of real-space electronic order. For the cuprates, despite several proposals, the emergence of order in the phase diagram between the commensurate antiferromagnetic state and the superconducting state is not well understood. Here we show that in this regime doped holes assemble in ‘electronic polymers'. Within a Monte Carlo study, we find that in clean systems by lowering the temperature the polymer melt condenses first in a smectic state and then in a Wigner crystal both with the addition of inversion symmetry breaking. Disorder blurs the positional order leaving a robust inversion symmetry breaking and a nematic order, accompanied by vector chiral spin order and with the persistence of a thermodynamic transition. Such electronic phases, whose properties are reminiscent of soft-matter physics, produce charge and spin responses in good accord with experiments. High-Tc superconductivity is thought to be associated with spatial electronic ordering, which for cuprates is not well understood yet. Here the authors use Monte Carlo simulations to show the emergence of a soft-matter-like electronic phase between the antiferromagnetic and the superconducting states.
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17
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Strečka J, Ekiz C. Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052143. [PMID: 26066155 DOI: 10.1103/physreve.91.052143] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2015] [Indexed: 06/04/2023]
Abstract
The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three interconnected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes upon increasing the coordination number of the underlying Husimi lattice.
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Affiliation(s)
- Jozef Strečka
- Department of Theoretical Physics and Astrophysics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovak Republic
| | - Cesur Ekiz
- Department of Physics, Faculty of Science and Letter, Adnan Menderes University, 09010 Aydın, Turkey
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Han M, Hyun J, Sim E. Formation of Rigid Organic Nanotubes with Controlled Internal Cavity Based on Frustrated Aggregate Internal Rearrangement Mechanism. J Phys Chem B 2013; 117:7763-70. [DOI: 10.1021/jp4015564] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Minwoo Han
- Department of Chemistry and Institute
of Nano-Bio Molecular
Assemblies, Yonsei University, 50 Yonsei-ro
Seodaemun-gu, Seoul 120-749, Korea
| | - Jungin Hyun
- Department of Chemistry and Institute
of Nano-Bio Molecular
Assemblies, Yonsei University, 50 Yonsei-ro
Seodaemun-gu, Seoul 120-749, Korea
| | - Eunji Sim
- Department of Chemistry and Institute
of Nano-Bio Molecular
Assemblies, Yonsei University, 50 Yonsei-ro
Seodaemun-gu, Seoul 120-749, Korea
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19
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Weber JK, Pande VS. Derivation and assessment of phase-shifted, disordered vector field models for frustrated solvent interactions. J Chem Phys 2013; 138:085103. [PMID: 23464179 PMCID: PMC3598771 DOI: 10.1063/1.4792638] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2012] [Accepted: 02/04/2013] [Indexed: 11/14/2022] Open
Abstract
The structure and properties of water at biological interfaces differ drastically from bulk due to effects including confinement and the presence of complicated charge distributions. This non-bulk-like behavior generally arises from water frustration, wherein all favorable interactions among water molecules cannot be simultaneously satisfied. While the frustration of interfacial water is ubiquitous in the cell, the role this frustration plays in mediating biophysical processes like protein folding is not well understood. To investigate the impact of frustration at interfaces, we here derive a general field theoretic model for the interaction of bulk and disordered vector fields at an embedded surface. We calculate thermodynamic and correlation functions for the model in two and three dimensions, and we compare our results to Monte Carlo simulations of lattice system analogs. In our analysis, we see that field-field cross correlations near the interface in the model give rise to a loss in entropy like that seen in glassy systems. We conclude by assessing our theory's utility as a coarse-grained model for water at polar biological interfaces.
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Affiliation(s)
- Jeffrey K Weber
- Department of Chemistry, Stanford University, Stanford, California 94305-4401, USA
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20
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LaForge AD, Pulido SH, Cava RJ, Chan BC, Ramirez AP. Quasispin glass in a geometrically frustrated magnet. PHYSICAL REVIEW LETTERS 2013; 110:017203. [PMID: 23383834 DOI: 10.1103/physrevlett.110.017203] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2012] [Indexed: 06/01/2023]
Abstract
The spin glass state in the spinel ZnCr(2(1-x))Ga(2x)O(4) is studied with magnetization and specific heat for x < 0.05. The freezing temperature is independent of disorder, despite a two-level-like density of states that varies linearly with x. This relationship implies the energy scale for freezing is independent of disorder, in contrast to mean field theories of spin glass. We suggest that the degrees of freedom are shielded spin vacancies, quasispins, which interact via an emergent long-range force mediated by the frustrated spin background.
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Affiliation(s)
- A D LaForge
- University of California, Santa Cruz, 1156 High Street, Santa Cruz, California 95064, USA
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21
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Wenzel S, Coletta T, Korshunov SE, Mila F. Evidence for columnar order in the fully frustrated transverse field Ising model on the square lattice. PHYSICAL REVIEW LETTERS 2012; 109:187202. [PMID: 23215324 DOI: 10.1103/physrevlett.109.187202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2012] [Indexed: 06/01/2023]
Abstract
Using extensive classical and quantum Monte Carlo simulations, we investigate the ground-state phase diagram of the fully frustrated transverse field Ising model on the square lattice. We show that pure columnar order develops in the low-field phase above a surprisingly large length scale, below which an effective U(1) symmetry is present. The same conclusion applies to the quantum dimer model with purely kinetic energy, to which the model reduces in the zero-field limit, as well as to the stacked classical version of the model. By contrast, the 2D classical version of the model is shown to develop plaquette order. Semiclassical arguments show that the transition from plaquette to columnar order is a consequence of quantum fluctuations.
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Affiliation(s)
- Sandro Wenzel
- Institute of Theoretical Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
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22
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Hoang DT, Diep HT. Hexagonal-close-packed lattice: Ground state and phase transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041107. [PMID: 22680420 DOI: 10.1103/physreve.85.041107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2011] [Indexed: 06/01/2023]
Abstract
We study the ground state (GS) and the phase transition in a hexagonal-close-packed lattice with both XY and Ising models by using extensive Monte Carlo simulation. We suppose the in-plane interaction J1 and interplane interaction J2, both antiferromagnetic. The system is frustrated with two kinds of GS configuration below and above a critical value of η=J1/J2 (ηc). For the Ising case, one has ηc=0.5 which separates in-plane ferromagnetic and antiferromagnetic states, while for the XY case ηc=1/3 separates the collinear and noncollinear spin configurations. The phase transition is shown to be of first (second) order for η>(<)ηc. The phase diagram in the space (η,T) is shown for both cases.
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Affiliation(s)
- Danh-Tai Hoang
- Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 8089 and 2, Avenue Adolphe Chauvin, F-95302 Cergy-Pontoise Cedex, France.
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23
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Giampaolo SM, Gualdi G, Monras A, Illuminati F. Characterizing and quantifying frustration in quantum many-body systems. PHYSICAL REVIEW LETTERS 2011; 107:260602. [PMID: 22243147 DOI: 10.1103/physrevlett.107.260602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2011] [Indexed: 05/31/2023]
Abstract
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.
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Affiliation(s)
- S M Giampaolo
- Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy
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24
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Bermudez A, Almeida J, Schmidt-Kaler F, Retzker A, Plenio MB. Frustrated quantum spin models with cold Coulomb crystals. PHYSICAL REVIEW LETTERS 2011; 107:207209. [PMID: 22181770 DOI: 10.1103/physrevlett.107.207209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2011] [Indexed: 05/31/2023]
Abstract
We exploit the geometry of a zigzag cold-ion crystal in a linear trap to propose the quantum simulation of a paradigmatic model of long-ranged magnetic frustration. Such a quantum simulation would clarify the complex features of a rich phase diagram that presents ferromagnetic, dimerized-antiferromagnetic, paramagnetic, and floating phases, together with previously unnoticed features that are hard to assess by numerics. We analyze in detail its experimental feasibility, and provide supporting numerical evidence on the basis of realistic parameters in current ion-trap technology.
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Affiliation(s)
- A Bermudez
- Institut für Theoretische Physik, Universität Ulm, Germany
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25
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Thomas CK, Katzgraber HG. Simplest model to study reentrance in physical systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:040101. [PMID: 22181076 DOI: 10.1103/physreve.84.040101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2011] [Revised: 06/07/2011] [Indexed: 05/31/2023]
Abstract
We numerically investigate the necessary ingredients for reentrant behavior in the phase diagram of physical systems. Studies on the possibly simplest model that exhibits reentrance, the two-dimensional random-bond Ising model, show that reentrant behavior is generic whenever frustration is present in the model. For both discrete and continuous disorder distributions, the phase diagram in the disorder-temperature plane is found to be reentrant, where for some disorder strengths a paramagnetic phase exists at both high and low temperatures, but an ordered ferromagnetic phase exists for intermediate temperatures.
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Affiliation(s)
- Creighton K Thomas
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
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26
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Piovesana O, Chiari B, Cinti A, Sulpice A. Synthesis, Structure, and Magnetic Properties of Cu2L2Cl2 (LH = N-Salicylidene-1,2-ethanediamine) - A New S = 1/2 Spin-Liquid Candidate. Eur J Inorg Chem 2011. [DOI: 10.1002/ejic.201100254] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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27
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Ngo VT, Hoang DT, Diep HT. Flat energy-histogram simulation of the phase transition in an Ising fully frustrated lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:226002. [PMID: 21572223 DOI: 10.1088/0953-8984/23/22/226002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We show in this paper the results of the phase transition of the so-called fully frustrated simple cubic lattice with the Ising spin model. We use here the Monte Carlo method with the flat energy-histogram Wang-Landau technique which is very powerful for detecting weak first-order phase transition. We show that the phase transition is clearly of first order, providing an answer to a question raised 25 years ago.
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28
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Ngo VT, Hoang DT, Diep HT. First-order transition in the XY model on a fully frustrated simple cubic lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041123. [PMID: 21230254 DOI: 10.1103/physreve.82.041123] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2010] [Indexed: 05/30/2023]
Abstract
We study the nature of the phase transition in the fully frustrated simple cubic lattice with the XY spin model. This system is the Villain's model generalized in three dimensions. The ground state is very particular with a 12-fold degeneracy. Previous studies have shown unusual critical properties. With the powerful Wang-Landau flat-histogram Monte Carlo method, we carry out in this work intensive simulations with very large lattice sizes. We show that the phase transition is clearly of first order, putting an end to the uncertainty which has lasted for more than 20 years.
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Affiliation(s)
- V Thanh Ngo
- Institute of Physics, P.O. Box 429, Bo Ho, Hanoi 10000, Vietnam
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29
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Otsuka H. Classical dimer model with anisotropic interactions on the square lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:011140. [PMID: 19658686 DOI: 10.1103/physreve.80.011140] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2009] [Indexed: 05/28/2023]
Abstract
We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalization calculations of the nonsymmetric real transfer matrices up to linear dimension specified by L=20 and determine the global phase diagram. For the repulsive region, we find the boundary between the dimer-liquid and the strong repulsion phases. Based on the dispersion relation of the one-string motion, which exhibits a twofold "zero-energy flat band" in the strong repulsion limit, we give an intuitive account for the property of the strong repulsion phase.
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Affiliation(s)
- Hiromi Otsuka
- Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan
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30
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Baek SK, Shima H, Kim BJ. Curvature-induced frustration in the XY model on hyperbolic surfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:060106. [PMID: 19658458 DOI: 10.1103/physreve.79.060106] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2008] [Indexed: 05/28/2023]
Abstract
We study low-temperature properties of the XY spin model on a negatively curved surface. Geometric curvature of the surface gives rise to frustration in local spin configuration, which results in the formation of high-energy spin clusters scattered over the system. Asymptotic behavior of the spin-glass susceptibility suggests a zero-temperature glass transition, which is attributed to multiple optimal configurations of spin clusters due to nonzero surface curvature of the system. It implies that a constant ferromagnetic spin interaction on a regular lattice can exhibit glasslike behavior without possessing any disorder if the lattice is put on top of a negatively curved space such as a hyperbolic surface.
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Affiliation(s)
- Seung Ki Baek
- Department of Physics, Umeå University, 901 87 Umeå, Sweden.
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31
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Haraldsen JT, Fishman RS. Spin rotation technique for non-collinear magnetic systems: application to the generalized Villain model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:216001. [PMID: 21825566 DOI: 10.1088/0953-8984/21/21/216001] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
This work develops a generalized technique for determining the static and dynamic properties of any non-collinear magnetic system. By rotating the spin operators into the local spin reference frame, we evaluate the zeroth, first, and second order terms in a Holstein-Primakoff expansion, and through a Green's functions approach, we determine the structure factor intensities for the spin-wave frequencies. To demonstrate this technique, we examine the spin-wave dynamics of the generalized Villain model with a varying interchain interaction. The new interchain coupling expands the overall phase diagram with the realization of two non-equivalent canted spin configurations. The rotational Holstein-Primakoff expansion provides both analytical and numerical results for the spin dynamics and intensities of these phases.
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Affiliation(s)
- J T Haraldsen
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
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32
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Muguruma C, Okamoto Y, Berg BA. Thermodynamics of two lattice ice models in three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:041113. [PMID: 18999385 DOI: 10.1103/physreve.78.041113] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2008] [Indexed: 05/27/2023]
Abstract
In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature, beta=0 ). (B) Both ice rules hold for ground-state configurations. This allowed for an efficient calculation of the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. Here we present the thermodynamics of these models in more details. Despite their similarities with Potts models, no sign of a disorder-order phase transition is found.
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Affiliation(s)
- Chizuru Muguruma
- School of International Liberal Studies, Chukyo University, Toyota, Aichi, Japan
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Garlea VO, Jin R, Mandrus D, Roessli B, Huang Q, Miller M, Schultz AJ, Nagler SE. Magnetic and orbital ordering in the spinel MnV2O4. PHYSICAL REVIEW LETTERS 2008; 100:066404. [PMID: 18352495 DOI: 10.1103/physrevlett.100.066404] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2007] [Indexed: 05/26/2023]
Abstract
Neutron inelastic scattering and diffraction techniques have been used to study the MnV2O4 spinel system. Our measurements show the existence of two transitions to long-range ordered ferrimagnetic states, the first collinear and the second noncollinear. The lower temperature transition, characterized by development of antiferromagnetic components in the basal plane, is accompanied by a tetragonal distortion and the appearance of a gap in the magnetic excitation spectrum. The low-temperature noncollinear magnetic structure has been definitively resolved. Taken together, the crystal and magnetic structures indicate a staggered ordering of the V d orbitals. The anisotropy gap is a consequence of unquenched V orbital angular momentum.
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Affiliation(s)
- V O Garlea
- Neutron Scattering Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.
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34
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Yoon J, Solomon EI. Electronic structures of exchange coupled trigonal trimeric Cu(II) complexes: Spin frustration, antisymmetric exchange, pseudo-A terms, and their relation to O2 activation in the multicopper oxidases. Coord Chem Rev 2007. [DOI: 10.1016/j.ccr.2006.04.012] [Citation(s) in RCA: 121] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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35
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Polini M, Fazio R, MacDonald AH, Tosi MP. Realization of fully frustrated Josephson-junction arrays with cold atoms. PHYSICAL REVIEW LETTERS 2005; 95:010401. [PMID: 16090587 DOI: 10.1103/physrevlett.95.010401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2005] [Indexed: 05/03/2023]
Abstract
Fully frustrated Josephson-junction arrays (FF-JJA's) exhibit a subtle compound phase transition in which an Ising transition associated with discrete broken translational symmetry and a Berezinskii-Kosterlitz-Thouless transition associated with quasi-long-range phase coherence occur nearly simultaneously. In this Letter we discuss a cold-atom realization of the FF-JJA system. We demonstrate that both orders can be studied by standard momentum-distribution-function measurements and present numerical results, based on a successful self-consistent spin-wave approximation, that illustrate the expected behavior of observables.
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Affiliation(s)
- Marco Polini
- NEST-INFM and Classe di Scienze, Scuola Normale Superiore, I-56126 Pisa, Italy.
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36
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Wei H, Wang B, Chen Z. Magnetic exchange of trinuclear spin frustration system: CASPT2 and density functional theory study on hydroxo-bridged chromium complex [Cr3(NH3)10(OH)4]·Br5. Chem Phys Lett 2005. [DOI: 10.1016/j.cplett.2005.03.080] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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37
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Konar S, Mukherjee PS, Zangrando E, Drew MG, Diaz C, Ribas J, Chaudhuri NR. A new porous 2D coordination polymer built by copper(II) and trimesic acid. Inorganica Chim Acta 2005. [DOI: 10.1016/j.ica.2004.08.010] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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38
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Korshunov SE, Douçot B. Fluctuations and vortex-pattern ordering in the fully frustrated XY model on a honeycomb lattice. PHYSICAL REVIEW LETTERS 2004; 93:097003. [PMID: 15447130 DOI: 10.1103/physrevlett.93.097003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2003] [Indexed: 05/24/2023]
Abstract
The accidental degeneracy of various ground states of a fully frustrated XY model with a honeycomb lattice is shown to survive even when the free energy of the harmonic fluctuations is taken into account. The reason for that consists in the existence of a hidden gauge symmetry between the Hamiltonians describing the harmonic fluctuations in all these ground states. A particular vortex pattern is selected only when anharmonic fluctuations are taken into account. However, the observation of vortex ordering requires relatively large system size L>>Lc > or approximately equal to 10(5).
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Affiliation(s)
- S E Korshunov
- L. D. Landau Institute for Theoretical Physics, Kosygina 2, Moscow 119334, Russia
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39
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Kim E, Kim B, Lee SJ. Nonequilibrium critical dynamics of the triangular antiferromagnetic Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:066127. [PMID: 14754289 DOI: 10.1103/physreve.68.066127] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2003] [Revised: 08/29/2003] [Indexed: 05/24/2023]
Abstract
We investigate the nonequilibrium critical dynamics of antiferromagnetic Ising model on a two-dimensional triangular lattice via dynamic Monte Carlo simulation employing spin-flip kinetics. Macroscopic degeneracy of the ground state originating from geometric frustration fundamentally affects the nonequilibrium dynamics of the system. In particular, the defects and the loose spins (whose flip costs no energy) play key roles in the dynamics. The long-time evolution is characterized by a critical dynamic scaling with a growing length scale xi(t). With random initial configurations, xi(t) exhibits a subdiffusive growth in time, xi(t) approximately t(1/z) with 1/z approximately 0.43, while xi(t) shows a diffusive growth with z=2 for the relaxation within the dominant sector of the ground-state manifold. The nonequilibrium critical dynamics therefore exhibits an interesting initial-state dependence. Persistence and the two-time temporal properties are also discussed.
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Affiliation(s)
- Eunhye Kim
- Department of Physics, Changwon National University, Changwon 641-773, Korea
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40
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Ko MK, Lee SJ, Lee J, Kim B. Vortex patterns and infinite degeneracy in the uniformly frustrated XY models and lattice Coulomb gas. PHYSICAL REVIEW E 2003; 67:046120. [PMID: 12786449 DOI: 10.1103/physreve.67.046120] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2002] [Indexed: 11/07/2022]
Abstract
We find analytically and numerically that there exist infinite degeneracies in the ground state vortex configurations of a uniformly frustrated XY model on a square lattice for cases of frustrations f=1/6, 1/7, 1/8, and 1/10. More generally, we could also obtain a class of exact solutions for the phase configurations corresponding to the cases of f=1/q=1/(2m) with an integer m>or=3 of which the above cases of m=3, 4, and 5 correspond to the true ground states. These states are analogous to the staircase solutions originally given by Halsey [Phys. Rev. B 31, 5728 (1985)], which, however, are relevant in a different regime of the frustration parameter (or vortex density). In these quasistaircase states, all the gauge-invariant phase differences are found to be integer multiples of pi/2q. The supercurrents are conserved at each node in a trivial manner by separate channels. The infinite ground state degeneracy is preserved in the case of an arbitrary screening length for the corresponding lattice Coulomb gas.
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41
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Lee DH, Wu FY. Duality relation for frustrated spin models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:026111. [PMID: 12636752 DOI: 10.1103/physreve.67.026111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2002] [Indexed: 05/24/2023]
Abstract
We consider discrete spin models on arbitrary planar graphs and lattices with frustrated interactions. We first analyze the Ising model with frustrated plaquettes. We use an algebraic approach to derive the result that an Ising model with some of its plaquettes frustrated has a dual model which is an Ising model with an external field ipi/2 applied to the dual sites centered at frustrated plaquettes. In the case where all plaquettes are frustrated, this leads to the known result that the dual model has a uniform field ipi/2, whose partition function can be evaluated in the thermodynamic limit for regular lattices. The analysis is extended to a Potts spin glass with analogous results obtained.
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Affiliation(s)
- D-H Lee
- Department of Physics, University of California, Berkeley, CA 94720, USA
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42
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Zhang W, Bruda S, Landee CP, Parent JL, Turnbull MM. Structures and magnetic properties of transition metal complexes of 1,3,5-benzenetricarboxylic acid. Inorganica Chim Acta 2003. [DOI: 10.1016/s0020-1693(02)01139-8] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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43
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Korshunov SE. Kink pairs unbinding on domain walls and the sequence of phase transitions in fully frustrated XY models. PHYSICAL REVIEW LETTERS 2002; 88:167007. [PMID: 11955254 DOI: 10.1103/physrevlett.88.167007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2001] [Indexed: 05/23/2023]
Abstract
The unbinding of kink pairs on domain walls in the fully frustrated XY model (on square or triangular lattices) is shown to induce the vanishing of phase coupling across the walls. This forces the phase transition, associated with unbinding of vortex pairs, to take place at a lower temperature than the other phase transition, associated with proliferation of the Ising-type domain walls. The results are applicable for a description of superconducting junction arrays and wire networks in a perpendicular magnetic field, as well as of planar antiferromagnets with a triangular lattice.
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Affiliation(s)
- S E Korshunov
- L. D. Landau Institute for Theoretical Physics, Kosygina 2, Moscow 117940, Russia
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Shindou R, Nagaosa N. Orbital ferromagnetism and anomalous Hall effect in antiferromagnets on the distorted fcc lattice. PHYSICAL REVIEW LETTERS 2001; 87:116801. [PMID: 11531542 DOI: 10.1103/physrevlett.87.116801] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2001] [Indexed: 05/23/2023]
Abstract
The Berry phase due to the spin wave function gives rise to the orbital ferromagnetism and anomalous Hall effect in the noncoplanar antiferromagnetic ordered state on face-centered-cubic (fcc) lattice once the crystal is distorted perpendicular to the (1,1,1) or (1,1,0) plane. The relevance to the real systems gamma-FeMn and NiS2 is also discussed.
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Affiliation(s)
- R Shindou
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo, 113-8656 Japan
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45
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Villain J. Two-level systems in a spin-glass model. I. General formalism and two-dimensional model. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0022-3719/10/23/013] [Citation(s) in RCA: 239] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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46
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Vannimenus J, Toulouse G. Theory of the frustration effect. II. Ising spins on a square lattice. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0022-3719/10/18/008] [Citation(s) in RCA: 236] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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47
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Bray AJ, Moore MA, Reed P. Vanishing of the Edwards-Anderson order parameter in two- and three-dimensional Ising spin glasses. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0022-3719/11/6/024] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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48
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Derrida B, Vannimenus J, Pomeau Y. Simple frustrated systems: chains, strips and squares. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0022-3719/11/23/019] [Citation(s) in RCA: 93] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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49
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Penson KA, Jullien R, Pfeuty P. Triangular antiferromagnetic Ising model with a transverse field at zero temperature. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0022-3719/12/19/015] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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50
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