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Lee SB, Kim JM. Continuum contact process and influence of impurity on the critical behavior in absorbing-state phase transitions in two dimensions. Phys Rev E 2023; 108:064135. [PMID: 38243520 DOI: 10.1103/physreve.108.064135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 11/22/2023] [Indexed: 01/21/2024]
Abstract
We study via Monte Carlo simulations the influence of quenched and mobile impurities in the contact process (CP) on two-dimensional lattice and continuum systems. In the lattice system, the effect of mobile impurity was studied for the density n_{i}=0.2 and two selected values of hopping probability for impurity particles, w=0.5 and 1. In the continuum system, the CP was defined by distributing spherical impurity particles of diameter σ_{i} and number density n_{i}=0.2 and active particles of diameter unity and number density 1-n_{i} on a square substrate with periodic boundaries. In each dynamic process, a particle is selected at random; the active particle either creates with a rate λ an offspring at a distance r (1≤r≤1.5) from the active particle or annihilates with a unit rate, and the impurity particle hops a distance r (0≤r≤1), both along randomly selected directions. We found that the lattice CP shows power-law behaviors with varying critical exponents depending on the values of w. For the continuum CP with quenched impurity, the critical behavior followed the activated scaling scenario, whereas with mobile impurity usual power-law behaviors were observed but the critical exponents varied depending on the values of σ_{i}.
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Affiliation(s)
- Sang Bub Lee
- Department of Physics and OMEG Institute, Soongsil University, Seoul 06978, Korea
| | - Jin Min Kim
- Department of Physics and OMEG Institute, Soongsil University, Seoul 06978, Korea
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2
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Kovács IA, Iglói F. Geometry of rare regions behind Griffiths singularities in random quantum magnets. Sci Rep 2022; 12:1074. [PMID: 35058527 PMCID: PMC8776845 DOI: 10.1038/s41598-022-05096-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 12/24/2021] [Indexed: 12/04/2022] Open
Abstract
In many-body systems with quenched disorder, dynamical observables can be singular not only at the critical point, but in an extended region of the paramagnetic phase as well. These Griffiths singularities are due to rare regions, which are locally in the ordered phase and contribute to a large susceptibility. Here, we study the geometrical properties of rare regions in the transverse Ising model with dilution or with random couplings and transverse fields. In diluted models, the rare regions are percolation clusters, while in random models the ground state consists of a set of spin clusters, which are calculated by the strong disorder renormalization method. We consider the so called energy cluster, which has the smallest excitation energy and calculate its mass and linear extension in one-, two- and three-dimensions. Both average quantities are found to grow logarithmically with the linear size of the sample. Consequently, the energy clusters are not compact: for the diluted model they are isotropic and tree-like, while for the random model they are quasi-one-dimensional.
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Affiliation(s)
- István A Kovács
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA.
- Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL, 60208, USA.
| | - Ferenc Iglói
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, Budapest, 1525, Hungary
- Institute of Theoretical Physics, Szeged University, Szeged, 6720, Hungary
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3
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Thompson F, Singh RRP. Griffiths-McCoy singularities in the dilute transverse-field Ising model: A numerical linked cluster expansion study. Phys Rev E 2019; 99:032129. [PMID: 30999511 DOI: 10.1103/physreve.99.032129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Indexed: 11/07/2022]
Abstract
We use numerical linked cluster expansions (NLCEs) to study the site-diluted transverse-field Ising model on the square lattice at T=0. NLCE with a self-consistent mean field on the boundary of the clusters is used to obtain the ground-state magnetization, susceptibility, and structure factor as a function of transverse field h and exchange constant J. Adding site dilution to the model turns NLCE into a series expansion in the dilution parameter p. Studying the divergence of the structure factor allows us to establish the phase diagram in the h/J and p plane. By studying the magnetization of the system in a longitudinal field, we investigate the Griffiths-McCoy singularities. We find that the magnetization develops nonlinearities in the Griffiths phase with exponents that vary continuously with h. Additionally, the probability distribution of the local susceptibility develops long tails in the Griffiths phase, which is studied in terms of its moments.
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Affiliation(s)
- Foster Thompson
- Department of Physics, Case Western Reserve University, Ohio 44106, USA
| | - Rajiv R P Singh
- Department of Physics, University of California Davis, California 95616, USA
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4
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Wang R, Gebretsadik A, Ubaid-Kassis S, Schroeder A, Vojta T, Baker PJ, Pratt FL, Blundell SJ, Lancaster T, Franke I, Möller JS, Page K. Quantum Griffiths Phase Inside the Ferromagnetic Phase of Ni_{1-x}V_{x}. PHYSICAL REVIEW LETTERS 2017; 118:267202. [PMID: 28707923 DOI: 10.1103/physrevlett.118.267202] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2016] [Indexed: 06/07/2023]
Abstract
We study by means of bulk and local probes the d-metal alloy Ni_{1-x}V_{x} close to the quantum critical concentration, x_{c}≈11.6%, where the ferromagnetic transition temperature vanishes. The magnetization-field curve in the ferromagnetic phase takes an anomalous power-law form with a nonuniversal exponent that is strongly x dependent and mirrors the behavior in the paramagnetic phase. Muon spin rotation experiments demonstrate inhomogeneous magnetic order and indicate the presence of dynamic fluctuating magnetic clusters. These results provide strong evidence for a quantum Griffiths phase on the ferromagnetic side of the quantum phase transition.
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Affiliation(s)
- Ruizhe Wang
- Physics Department, Kent State University, Kent, Ohio 44242, USA
| | | | | | - Almut Schroeder
- Physics Department, Kent State University, Kent, Ohio 44242, USA
| | - Thomas Vojta
- Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - Peter J Baker
- ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Oxford, Oxfordshire OX11 0QX, United Kingdom
| | - Francis L Pratt
- ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Oxford, Oxfordshire OX11 0QX, United Kingdom
| | - Stephen J Blundell
- Clarendon Laboratory, Department of Physics, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Tom Lancaster
- Clarendon Laboratory, Department of Physics, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Isabel Franke
- Clarendon Laboratory, Department of Physics, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Johannes S Möller
- Clarendon Laboratory, Department of Physics, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Katharine Page
- Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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5
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Orth PP, Fernandes RM, Walter J, Leighton C, Shklovskii BI. Percolation via Combined Electrostatic and Chemical Doping in Complex Oxide Films. PHYSICAL REVIEW LETTERS 2017; 118:106801. [PMID: 28339226 DOI: 10.1103/physrevlett.118.106801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Indexed: 06/06/2023]
Abstract
Stimulated by experimental advances in electrolyte gating methods, we investigate theoretically percolation in thin films of inhomogeneous complex oxides, such as La_{1-x}Sr_{x}CoO_{3} (LSCO), induced by a combination of bulk chemical and surface electrostatic doping. Using numerical and analytical methods, we identify two mechanisms that describe how bulk dopants reduce the amount of electrostatic surface charge required to reach percolation: (i) bulk-assisted surface percolation and (ii) surface-assisted bulk percolation. We show that the critical surface charge strongly depends on the film thickness when the film is close to the chemical percolation threshold. In particular, thin films can be driven across the percolation transition by modest surface charge densities. If percolation is associated with the onset of ferromagnetism, as in LSCO, we further demonstrate that the presence of critical magnetic clusters extending from the film surface into the bulk results in considerable enhancement of the saturation magnetization, with pronounced experimental consequences. These results should significantly guide experimental work seeking to verify gate-induced percolation transitions in such materials.
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Affiliation(s)
- Peter P Orth
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Rafael M Fernandes
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Jeff Walter
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - C Leighton
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - B I Shklovskii
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
- Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
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6
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Vojta T. Strong-disorder magnetic quantum phase transitions: Status and new developments. ACTA ACUST UNITED AC 2014. [DOI: 10.1088/1742-6596/529/1/012016] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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7
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Vojta T, Hoyos JA. Criticality and quenched disorder: Harris criterion versus rare regions. PHYSICAL REVIEW LETTERS 2014; 112:075702. [PMID: 24579616 DOI: 10.1103/physrevlett.112.075702] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2013] [Indexed: 06/03/2023]
Abstract
We employ scaling arguments and optimal fluctuation theory to establish a general relation between quantum Griffiths singularities and the Harris criterion for quantum phase transitions in disordered systems. If a clean critical point violates the Harris criterion, it is destabilized by weak disorder. At the same time, the Griffiths dynamical exponent z' diverges upon approaching the transition, suggesting unconventional critical behavior. In contrast, if the Harris criterion is fulfilled, power-law Griffiths singularities can coexist with clean critical behavior, but z' saturates at a finite value. We present applications of our theory to a variety of systems including quantum spin chains, classical reaction-diffusion systems and metallic magnets, and we discuss modifications for transitions above the upper critical dimension. Based on these results we propose a unified classification of phase transitions in disordered systems.
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Affiliation(s)
- Thomas Vojta
- Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - José A Hoyos
- Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, São Carlos, São Paulo 13560-970, Brazil
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8
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Lee MY, Vojta T. Absorbing-state phase transitions on percolating lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:041112. [PMID: 19518178 DOI: 10.1103/physreve.79.041112] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2009] [Indexed: 05/27/2023]
Abstract
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical percolation theory with the properties of the supercritical nonequilibrium system on a finite-size cluster. In the case of the contact process, the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a different universality class. The critical point is characterized by ultraslow activated dynamical scaling and accompanied by strong Griffiths singularities. To confirm the universality of this exotic scaling scenario we also study the generalized contact process with several (symmetric) absorbing states and we support our theory by extensive Monte Carlo simulations.
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Affiliation(s)
- Man Young Lee
- Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
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9
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Ancona-Torres C, Silevitch DM, Aeppli G, Rosenbaum TF. Quantum and classical glass transitions in LiHoxY1-xF4. PHYSICAL REVIEW LETTERS 2008; 101:057201. [PMID: 18764428 DOI: 10.1103/physrevlett.101.057201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2008] [Revised: 04/02/2008] [Indexed: 05/26/2023]
Abstract
When performed in the proper low-field, low-frequency limits, measurements of the dynamics and the nonlinear susceptibility in the model Ising magnet in a transverse field LiHo(x)Y(1-x)F(4) prove the existence of a spin-glass transition for x=0.167 and 0.198. The classical behavior tracks for the two concentrations, but the behavior in the quantum regime at large transverse fields differs because of the competing effects of quantum entanglement and random fields.
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Affiliation(s)
- C Ancona-Torres
- The James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637, USA
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10
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Hoyos JA, Vojta T. Theory of smeared quantum phase transitions. PHYSICAL REVIEW LETTERS 2008; 100:240601. [PMID: 18643562 DOI: 10.1103/physrevlett.100.240601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2008] [Indexed: 05/26/2023]
Abstract
We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.
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Affiliation(s)
- José A Hoyos
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
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11
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Lin YC, Iglói F, Rieger H. Entanglement entropy at infinite-randomness fixed points in higher dimensions. PHYSICAL REVIEW LETTERS 2007; 99:147202. [PMID: 17930713 DOI: 10.1103/physrevlett.99.147202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2007] [Indexed: 05/25/2023]
Abstract
The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong-disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite-randomness fixed point in the diluted transverse Ising model in higher dimensions.
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Affiliation(s)
- Yu-Cheng Lin
- Theoretische Physik, Universität des Saarlandes, 66041, Saarbrücken, Germany
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12
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Sandvik AW. Quantum criticality and percolation in dimer-diluted two-dimensional antiferromagnets. PHYSICAL REVIEW LETTERS 2006; 96:207201. [PMID: 16803199 DOI: 10.1103/physrevlett.96.207201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2006] [Indexed: 05/10/2023]
Abstract
The S = 1/2 Heisenberg model is considered on bilayer and single-layer square lattices with couplings J1, J2, with each spin belonging to one J2-coupled dimer. A transition from a Néel to disordered ground state occurs at a critical value of g = J2/J1. The systems are here studied at their dimer-dilution percolation points p*. The multicritical point (g*,p*) previously found for the bilayer is not reproduced for the single layer. Instead, there is a line of critical points (g < g*, p*) with continuously varying exponents. The uniform magnetic susceptibility diverges as T(-alpha) with alpha element of [1/2,1]. This unusual behavior is attributed to an effective free-moment density approximately T(1-alpha). The susceptibility of the bilayer is not divergent but exhibits remarkably robust quantum-critical scaling.
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Affiliation(s)
- Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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13
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Vojta T. Rare region effects at classical, quantum and nonequilibrium phase transitions. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/22/r01] [Citation(s) in RCA: 316] [Impact Index Per Article: 17.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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14
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Vojta T, Lee MY. Nonequilibrium phase transition on a randomly diluted lattice. PHYSICAL REVIEW LETTERS 2006; 96:035701. [PMID: 16486731 DOI: 10.1103/physrevlett.96.035701] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2005] [Indexed: 05/06/2023]
Abstract
We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation threshold of the lattice is characterized by unconventional activated (exponential) dynamical scaling and strong Griffiths effects. We calculate the critical behavior in two and three space dimensions, and we also relate our results to the recently found infinite-randomness fixed point in the disordered one-dimensional contact process.
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Affiliation(s)
- Thomas Vojta
- Department of Physics, University of Missouri-Rolla, Rolla, Missouri 65409, USA
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15
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Vojta T, Schmalian J. Percolation quantum phase transitions in diluted magnets. PHYSICAL REVIEW LETTERS 2005; 95:237206. [PMID: 16384338 DOI: 10.1103/physrevlett.95.237206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2005] [Indexed: 05/05/2023]
Abstract
We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La2Cu(1-p)(Zn,Mg)(p)O4. Our results are also relevant for disordered interacting boson systems.
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Affiliation(s)
- Thomas Vojta
- Department of Physics, University of Missouri-Rolla, Rolla, Missouri 65409, USA
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16
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Dobrosavljević V, Miranda E. Absence of conventional quantum phase transitions in itinerant systems with disorder. PHYSICAL REVIEW LETTERS 2005; 94:187203. [PMID: 15904407 DOI: 10.1103/physrevlett.94.187203] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2004] [Indexed: 05/02/2023]
Abstract
Effects of disorder are examined in itinerant systems close to quantum critical points. We argue that spin fluctuations due to the long-range part of the RKKY interactions generically induce non-Ohmic dissipation due to rare disorder configurations. This dissipative mechanism is found to destabilize quantum Griffiths phase behavior in itinerant systems with arbitrary symmetry of the order parameter, leading to the formation of a "cluster glass" phase preceding uniform ordering.
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Affiliation(s)
- V Dobrosavljević
- Department of Physics and National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32306, USA
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17
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Sknepnek R, Vojta T, Vojta M. Exotic versus conventional scaling and universality in a disordered bilayer quantum heisenberg antiferromagnet. PHYSICAL REVIEW LETTERS 2004; 93:097201. [PMID: 15447133 DOI: 10.1103/physrevlett.93.097201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2004] [Indexed: 05/24/2023]
Abstract
We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.
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Affiliation(s)
- Rastko Sknepnek
- Physics Department, University of Missouri, Rolla, Rolla, Missouri 65409, USA
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18
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Galitski VM, Kaminski A, Das Sarma S. Griffiths phase in diluted magnetic semiconductors. PHYSICAL REVIEW LETTERS 2004; 92:177203. [PMID: 15169188 DOI: 10.1103/physrevlett.92.177203] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2003] [Indexed: 05/24/2023]
Abstract
We study the effects of disorder in the vicinity of the ferromagnetic transition in a diluted magnetic semiconductor in the strongly localized regime. We derive an effective polaron Hamiltonian, which leads to the Griffiths phase above the ferromagnetic transition point. The Griffiths-McCoy effects yield nonperturbative contributions to the dynamic susceptibility. We explicitly derive the long-time susceptibility, which has a pseudoscaling form, with the dynamic critical exponent being expressed through the percolation indices.
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Affiliation(s)
- V M Galitski
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD 20742-4111, USA
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19
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Sandvik AW. Multicritical point in a diluted bilayer Heisenberg quantum antiferromagnet. PHYSICAL REVIEW LETTERS 2002; 89:177201. [PMID: 12398701 DOI: 10.1103/physrevlett.89.177201] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2002] [Indexed: 05/24/2023]
Abstract
The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed interlayer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multicritical point (p(*),g(*)) at the classical percolation density p=p(*) and interlayer coupling g(*) approximately equal 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero interlayer coupling and could be relevant for antiferromagnetic cuprates doped with nonmagnetic impurities.
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Affiliation(s)
- Anders W Sandvik
- Department of Physics, Abo Akademi University, Porthansgatan 3, FIN-20500 Turku, Finland
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20
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Vajk OP, Greven M. Quantum versus geometric disorder in a two-dimensional Heisenberg antiferromagnet. PHYSICAL REVIEW LETTERS 2002; 89:177202. [PMID: 12398702 DOI: 10.1103/physrevlett.89.177202] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2002] [Indexed: 05/24/2023]
Abstract
We present a numerical study of the spin-1/2 bilayer Heisenberg antiferromagnet with random interlayer dimer dilution. From the temperature dependence of the uniform susceptibility and a scaling analysis of the spin correlation length we deduce the ground state phase diagram as a function of nonmagnetic impurity concentration p and bilayer coupling g. At the site percolation threshold, there exists a multicritical point at small but nonzero bilayer coupling g(m)=0.15(3). The magnetic properties of the single-layer material La(2)Cu(1-p)(Zn,Mg)(p)O4 near the percolation threshold appear to be controlled by the proximity to this new quantum critical point.
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Affiliation(s)
- O P Vajk
- Department of Physics, Stanford University, Stanford, California 94305, USA
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21
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Marqués MI, Gonzalo JA. Dynamic scaling in diluted systems: deactivation through thermal dilution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:056114. [PMID: 11414968 DOI: 10.1103/physreve.63.056114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2000] [Indexed: 05/23/2023]
Abstract
Activated scaling is confirmed to hold in transverse field-induced phase transitions of randomly diluted Ising systems. Quantum Monte Carlo calculations have been made not just at the percolation threshold (pc) but also well below and above it. We follow the evolution of the activated scaling at zero temperature in the phase transition from ferromagnetic to quantum Griffiths phase (p>pc) at the phase boundary (p=pc) and for transitions inside the nonferromagnetic quantum Griffiths phase (p<pc). A novel deactivation phenomenon inside the nonferromagnetic Griffiths-McCoy phase (p<pc) is observed using a thermal (in contrast to random) dilution of the system.
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Affiliation(s)
- M I Marqués
- Departamento de Física de Materiales C-IV, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
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