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Salas J. Phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet. Phys Rev E 2020; 102:032124. [PMID: 33076030 DOI: 10.1103/physreve.102.032124] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Accepted: 08/28/2020] [Indexed: 11/07/2022]
Abstract
In this paper we study the phase diagram of the five-state Potts antiferromagnet on the bisected-hexagonal lattice. This question is important since Delfino and Tartaglia recently showed that a second-order transition in a five-state Potts antiferromagnet is allowed, and the bisected-hexagonal lattice had emerged as a candidate for such a transition on numerical grounds. By using high-precision Monte Carlo simulations and two complementary analysis methods, we conclude that there is a finite-temperature first-order transition point. This one separates a paramagnetic high-temperature phase, and a low-temperature phase where five phases coexist. This phase transition is very weak in the sense that its latent heat (per edge) is two orders of magnitude smaller than that of other well-known weak first-order phase transitions.
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Affiliation(s)
- Jesús Salas
- Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, 28911 Leganés, Spain and Grupo de Teorías de Campos y Física Estadística, Associate Unit Instituto Gregorio Millán (UC3M)-Instituto de Estructura de la Materia (CSIC), Madrid, Spain
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2
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Lv JP, Deng Y, Jacobsen JL, Salas J, Sokal AD. Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations. Phys Rev E 2018; 97:040104. [PMID: 29758740 DOI: 10.1103/physreve.97.040104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Indexed: 06/08/2023]
Abstract
We provide a criterion based on graph duality to predict whether the three-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge c=1. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the three-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.
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Affiliation(s)
- Jian-Ping Lv
- Department of Physics, Anhui Normal University, Wuhu 241000, China
- Anhui Province Key Laboratory of Optoelectric Materials Science and Technology, Wuhu 241000, China
| | - Youjin Deng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jesper Lykke Jacobsen
- Laboratoire de Physique Théorique, Département de Physique de l'ENS, École Normale Supérieure, Sorbonne Université, CNRS, PSL Research University, 75005 Paris, France
- Sorbonne Université, École Normale Supérieure, CNRS, Laboratoire de Physique Théorique (LPT ENS), 75005 Paris, France
- Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - Jesús Salas
- Grupo de Modelización, Simulación Numérica y Matemática Industrial, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
- Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán, UC3M, Unidad Asociada al IEM-CSIC, Madrid, Spain
| | - Alan D Sokal
- Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
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Keesman R, Lamers J. Numerical study of the F model with domain-wall boundaries. Phys Rev E 2017; 95:052117. [PMID: 28618633 DOI: 10.1103/physreve.95.052117] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2017] [Indexed: 11/07/2022]
Abstract
We perform a numerical study of the F model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size as well as its asymptotics and leading finite-size corrections. To complement this picture we use a full lattice multicluster algorithm to study equilibrium properties of this model for systems of moderate size, up to L=512. We compare the energy to its exactly known large-L asymptotics. We investigate the model's infinite-order phase transition by means of finite-size scaling for an observable derived from the staggered polarization in order to test the method put forward in our recent joint work with Duine and Barkema. In addition we analyze local properties of the model. Our data are perfectly consistent with analytical expressions for the arctic curves. We investigate the structure inside the temperate region of the lattice, confirming the oscillations in vertex densities that were first observed by Syljuåsen and Zvonarev and recently studied by Lyberg et al. We point out "(anti)ferroelectric" oscillations close to the corresponding frozen regions as well as "higher-order" oscillations forming an intricate pattern with saddle-point-like features.
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Affiliation(s)
- Rick Keesman
- Instituut-Lorentz, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
| | - Jules Lamers
- Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Göteborg, Sweden
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Huang Y, Chen K, Deng Y, Jacobsen JL, Kotecký R, Salas J, Sokal AD, Swart JM. Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012136. [PMID: 23410312 DOI: 10.1103/physreve.87.012136] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2012] [Indexed: 06/01/2023]
Abstract
We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of q. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.
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Affiliation(s)
- Yuan Huang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
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Romano S, De Matteis G. Orientationally ordered phase produced by fully antinematic interactions: a simulation study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011703. [PMID: 21867192 DOI: 10.1103/physreve.84.011703] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2010] [Revised: 04/22/2011] [Indexed: 05/31/2023]
Abstract
We consider here a classical model, consisting of D(2h) symmetric particles, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbors. Two orthonormal triads define orientations of a pair of interacting particles; the simplest potential models proposed in the literature can be written as a linear combination involving the squares of the scalar products between corresponding unit vectors only, thus depending on three parameters, and making the interaction model rather versatile. A coupling constant with negative sign tends to keep the two interacting unit vectors parallel to each other, whereas a positive sign tends to keep them mutually orthogonal (antinematic coupling). We address here a special, extreme case of the above family, involving only antinematic couplings: more precisely, three antinematic terms whose coefficients are set to a common positive value (hence the name PPP model). The model under investigation produces a doubly degenerate pair ground state; the nearest-neighbor range of the interaction and the bipartite character of the lattice can propagate the pair ground state and increase the overall degeneracy, but without producing frustration. The model was investigated by a simplified molecular field treatment as well as by Monte Carlo simulation, whose results suggested a second-order transition to a low-temperature biaxially ordered phase; ground-state configurations producing orientational order have been selected by thermal fluctuations. The molecular field treatment also predicted a continuous transition, and was found to overestimate the transition temperature by a factor 2.
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Affiliation(s)
- Silvano Romano
- Dipartimento di Fisica A Volta, Università di Pavia, Via A Bassi 6, I-27100 Pavia, Italy.
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Kotecký R, Salas J, Sokal AD. Phase transition in the three-state Potts antiferromagnet on the diced lattice. PHYSICAL REVIEW LETTERS 2008; 101:030601. [PMID: 18764243 DOI: 10.1103/physrevlett.101.030601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2008] [Revised: 04/22/2008] [Indexed: 05/26/2023]
Abstract
We prove that the 3-state Potts antiferromagnet on the diced lattice (dual of the kagome lattice) has entropically driven long-range order at low temperatures (including zero). We then present Monte Carlo simulations, using a cluster algorithm, of the 3-state and 4-state models. The 3-state model has a phase transition to the high-temperature disordered phase at v=e;{J}-1=-0.860 599+/-0.000 004 that appears to be in the universality class of the 3-state Potts ferromagnet. The 4-state model is disordered throughout the physical region, including at zero temperature.
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Affiliation(s)
- Roman Kotecký
- Center for Theoretical Study, Charles University, Prague, Czech Republic
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Wozar C, Kaestner T, Wipf A, Heinzl T, Pozsgay B. Phase structure ofZ(3)-Polyakov-loop models. Int J Clin Exp Med 2006. [DOI: 10.1103/physrevd.74.114501] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Sánchez MC, Subías G, García J, Blasco J. Cooperative Jahn-Teller phase transition in LaMnO3 studied by X-ray absorption spectroscopy. PHYSICAL REVIEW LETTERS 2003; 90:045503. [PMID: 12570431 DOI: 10.1103/physrevlett.90.045503] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2002] [Indexed: 05/24/2023]
Abstract
The local structure of LaMnO3 across the Jahn-Teller (JT) transition at T(JT)=750 K was studied by means of x-ray absorption near edge structure and extended x-ray absorption fine structure at the Mn K-edge. Our results indicate a similar electronic local structure for Mn atoms above and below T(JT) and a dynamical tetragonal JT distortion of MnO6 octahedra above T(JT). The structural transition is originated by the ordering of tetragonally distorted octahedra. The entropy content of the transition is analyzed within the framework of the three-state Potts model with nearest neighbor antiferrodistortive coupling.
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Affiliation(s)
- M C Sánchez
- Instituto de Ciencia de Materiales de Aragón, Consejo Superior de Investigaciones Científicas y Universidad de Zaragoza, 50009 Zaragoza, Spain
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de Queiroz SLA. Finite-size investigation of scaling corrections in the square-lattice three-state Potts antiferromagnet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:056104. [PMID: 12059644 DOI: 10.1103/physreve.65.056104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2002] [Indexed: 05/23/2023]
Abstract
We investigate the finite-temperature corrections to scaling in the three-state square-lattice Potts antiferromagnet, close to the critical point at T=0. Numerical diagonalization of the transfer matrix on semi-infinite strips of width L sites, 4 < or = L < or = 14, yields finite-size estimates of the corresponding scaled gaps, which are extrapolated to L --> infinity. Owing to the characteristics of the quantities under study, we argue that the natural variable to consider is x identical with L e(-2 beta). For the extrapolated scaled gaps we show that square-root corrections, in the variable x, are present, and provide estimates for the numerical values of the amplitudes of the first- and second-order correction terms, for both the first and second scaled gaps. We also calculate the third scaled gap of the transfer matrix spectrum at T=0, and find an extrapolated value of the decay-of-correlations exponent, eta(3)=2.00(1). This is at odds with earlier predictions, to the effect that the third relevant operator in the problem would give eta(P(stagg))=3, corresponding to the staggered polarization.
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Affiliation(s)
- S L A de Queiroz
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro RJ, Brazil.
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Stoycheva AD, Singer SJ. Computer simulations of a two-dimensional system with competing interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:036706. [PMID: 11909306 DOI: 10.1103/physreve.65.036706] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2001] [Indexed: 05/23/2023]
Abstract
The results and methodology of large scale computer simulations of the two-dimensional dipolar Ising model with long-range interactions are reported. Systems as large as 117,649 particles were studied to elucidate the elementary excitations and phase diagram of two-dimensional systems, such as Langmuir monolayers, thin garnet films, and adsorbed films on solid surfaces, which spontaneously form patterns of stripes, bubbles, and intermediately shaped domains. The challenging numerical investigations of large scale systems with long-range interactions at low temperatures were made possible by combining the fast multipole method and a non-Metropolis Monte Carlo sampling technique. Our simulations provide evidence that, at sufficiently high ratios of the repulsive to the attractive coupling constant for the model, twofold stripe order in the systems of interest is lost through a defect-mediated mechanism. Heat capacity data and the excitations observed in our simulations as the system disorders indicate that it is most likely an instance of a Kosterlitz-Thouless phase transition. The results from simulations with and without external field are in excellent agreement with the predictions of an analytic scaling theory [A. D. Stoycheva and S. J. Singer, Phys. Rev. E 64, 016118 (2001)], confirming the phase diagram furnished by the analytic model. The scaling theory suggests that, under certain conditions, defect-mediated stripe melting may be supplanted by Ising like disordering within stripes for small repulsion strength. A qualitative discussion of a model that supports both disordering mechanisms is presented.
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Affiliation(s)
- Antitsa D Stoycheva
- Department of Chemistry, Ohio State University, 100 W. 18th Avenue, Columbus, Ohio 43210, USA
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Yamaguchi C, Okabe Y. Three-dimensional antiferromagneticq-state Potts models: application of the Wang-Landau algorithm. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/42/305] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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12
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Kim SY, Creswick RJ. Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:066107. [PMID: 11415173 DOI: 10.1103/physreve.63.066107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2000] [Revised: 01/16/2001] [Indexed: 05/23/2023]
Abstract
The Q-state Potts model can be extended to noninteger and even complex Q by expressing the partition function in the Fortuin-Kasteleyn (F-K) representation. In the F-K representation the partition function Z(Q,a) is a polynomial in Q and v=a-1 (a=e(betaJ)) and the coefficients of this polynomial, Phi(b,c), are the number of graphs on the lattice consisting of b bonds and c connected clusters. We introduce the random-cluster transfer matrix to compute Phi(b,c) exactly on finite square lattices with several types of boundary conditions. Given the F-K representation of the partition function we begin by studying the critical Potts model Z(CP)=Z(Q,a(c)(Q)), where a(c)(Q)=1+square root[Q]. We find a set of zeros in the complex w=square root[Q] plane that map to (or close to) the Beraha numbers for real positive Q. We also identify Q(c)(L), the value of Q for a lattice of width L above which the locus of zeros in the complex p=v/square root[Q] plane lies on the unit circle. By finite-size scaling we find that 1/Q(c)(L)-->0 as L-->infinity. We then study zeros of the antiferromagnetic (AF) Potts model in the complex Q plane and determine Q(c)(a), the largest value of Q for a fixed value of a below which there is AF order. We find excellent agreement with Baxter's conjecture Q(AF)(c)(a)=(1-a)(a+3). We also investigate the locus of zeros of the ferromagnetic Potts model in the complex Q plane and confirm that Q(FM)(c)(a)=(a-1)(2). We show that the edge singularity in the complex Q plane approaches Q(c) as Q(c)(L) approximately Q(c)+AL(-y(q)), and determine the scaling exponent y(q) for several values of Q. Finally, by finite-size scaling of the Fisher zeros near the antiferromagnetic critical point we determine the thermal exponent y(t) as a function of Q in the range 2</=Q</=3. Using data for lattices of size 3</=L</=8 we find that y(t) is a smooth function of Q and is well fitted by y(t)=(1+Au+Bu2)/(C+Du) where u=-(2/pi)cos(-1)(squareroot[Q]/2). For Q=3 we find y(t) approximately 0.6; however if we include lattices up to L=12 we find y(t) approximately 0.50(8) in rough agreement with a recent result of Ferreira and Sokal [J. Stat. Phys. 96, 461 (1999)].
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Affiliation(s)
- S Y Kim
- Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA.
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Worgotter F. Cluster update algorithm and recognition. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:R1461-R1464. [PMID: 11088703 DOI: 10.1103/physreve.62.r1461] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2000] [Indexed: 05/23/2023]
Abstract
We present a fast and robust cluster update algorithm that is especially efficient in implementing the task of image segmentation using the method of superparamagnetic clustering. We apply it to a Potts model with spin interactions that are are defined by gray-scale differences within the image. Motivated by biological systems, we introduce the concept of neural inhibition to the Potts model realization of the segmentation problem. Including the inhibition term in the Hamiltonian results in enhanced contrast and thereby significantly improves segmentation quality. As a second benefit we can, after equilibration, directly identify the image segments as the clusters formed by the clustering algorithm. To construct a subsequent spin configuration the algorithm performs the standard steps of (i) forming clusters and of (ii) updating the spins in a cluster simultaneously. As opposed to standard algorithms, however, we share the interaction energy between the two steps. Thus, the update probabilities are not independent of the interaction energies. As a consequence, we observe an acceleration of the relaxation by a factor of 10 compared to the Swendson and Wang [Phys. Rev. Lett. 58, 86 (1987)] procedure.
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Moore C, Nordahl MG, Minar N, Shalizi CR. Vortex dynamics and entropic forces in antiferromagnets and antiferromagnetic Potts models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:5344-51. [PMID: 11970403 DOI: 10.1103/physreve.60.5344] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/1999] [Revised: 07/27/1999] [Indexed: 04/18/2023]
Abstract
It is well known in models with an interface representation, such as the dimer model, the triangular Ising antiferromagnet, the six-vertex ice model, and the three-state antiferromagnetic Potts model on the square lattice, that topological defects of opposite charge are attracted with an entropically-driven Coulomb force. We examine the Potts model in detail, show explicitly how this force is felt through local fields, and calculate the defects' mobility. We then take two approaches to measuring this force numerically. First, we quench a random initial state to zero temperature and measure the density of defects rho(t) as a function of time. While this gives some evidence for a local force, we compare it with a free diffusion experiment, and show that the asymptotic decay of rho(t) depends on the initial distribution of defects rather than the forces between them. Second, we set up initial conditions with a single pair of vortices, and measure the force between them as a function of distance. This gives reasonable agreement with theory, although finite-size effects and a lack of ergodicity play a significant role.
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Affiliation(s)
- C Moore
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
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15
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Burton JK, Henley CL. A constrained Potts antiferromagnet model with an interface representation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/30/24/007] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Pelizzola A. Low-temperature phase of the three-state antiferromagnetic Potts model on the simple-cubic lattice. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:R5885-R5888. [PMID: 9965937 DOI: 10.1103/physreve.54.r5885] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Matveev V, Shrock R. Complex-temperature singularities in Potts models on the square lattice. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:6174-6185. [PMID: 9965837 DOI: 10.1103/physreve.54.6174] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Heilmann RK, Wang JS, Swendsen RH. Rotationally symmetric ordered phase in the three-state antiferromagnetic Potts model. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:2210-2212. [PMID: 9983712 DOI: 10.1103/physrevb.53.2210] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kundrotas PJ, Lapinskas S, Rosengren A. Phase transitions in the three-state antiferromagnetic Potts model. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:9166-9169. [PMID: 9979951 DOI: 10.1103/physrevb.52.9166] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Caracciolo S, Edwards RG, Ferreira SJ, Pelissetto A, Sokal AD. Extrapolating Monte Carlo simulations to infinite volume: Finite-size scaling at xi /L >> 1. PHYSICAL REVIEW LETTERS 1995; 74:2969-2972. [PMID: 10058070 DOI: 10.1103/physrevlett.74.2969] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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21
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Ferreira SJ, Sokal AD. Antiferromagnetic Potts models on the square lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:6727-6730. [PMID: 9977213 DOI: 10.1103/physrevb.51.6727] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kawashima N, Gubernatis JE. Dual Monte Carlo and cluster algorithms. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:1547-1559. [PMID: 9962798 DOI: 10.1103/physreve.51.1547] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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23
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Zhang GM, Yang CZ. Cluster Monte Carlo dynamics for the antiferromagnetic Ising model on a triangular lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:12546-12549. [PMID: 9975415 DOI: 10.1103/physrevb.50.12546] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Redinz JA, Curado EM. Potts antiferromagnetic model on a family of fractal lattices: Exact results for an unusual phase. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:6689-6697. [PMID: 10009389 DOI: 10.1103/physrevb.49.6689] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ueno Y, Kasono K. Incompletely ordered phases and phase transitions in the three-dimensional general clock model. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:16471-16483. [PMID: 10008229 DOI: 10.1103/physrevb.48.16471] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lubin M, Sokal AD. Comment on "Antiferromagnetic Potts models". PHYSICAL REVIEW LETTERS 1993; 71:1778. [PMID: 10054497 DOI: 10.1103/physrevlett.71.1778] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Fisch R. Ferromagnetism in the XY model with random threefold anisotropy. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:242-246. [PMID: 10002205 DOI: 10.1103/physrevb.46.242] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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30
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Kandel D, Domany E. General cluster Monte Carlo dynamics. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:8539-8548. [PMID: 9996485 DOI: 10.1103/physrevb.43.8539] [Citation(s) in RCA: 74] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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