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Jorge LN, Ferreira LS, Caparica AA. Three-dimensional Baxter-Wu model. Phys Rev E 2019; 100:032141. [PMID: 31640024 DOI: 10.1103/physreve.100.032141] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2018] [Indexed: 11/07/2022]
Abstract
A classic three-dimensional spin model, based upon the Baxter-Wu scheme, is presented. It is found, by entropic sampling simulations, that the behavior of the energy and magnetization fourth-order cumulants points to a first-order phase transition. A finite-size procedure was performed, confirming that the system scales with the dimensionality d=3, yielding a high-resolution estimate of the transition temperature as T_{c}=11.377485(29).
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Affiliation(s)
- L N Jorge
- Instituto Federal do Mato Grosso, Campus Cáceres, CEP. 78200-000, Cáceres, Mato Grosso, Brazil
| | - L S Ferreira
- Instituto de Física, Universidade Federal de Goiás, Av. Esperança s/n, 74.690-900, Goiânia, GO, Brazil
| | - A A Caparica
- Instituto de Física, Universidade Federal de Goiás, Av. Esperança s/n, 74.690-900, Goiânia, GO, Brazil
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Belletti F, Cotallo M, Cruz A, Fernandez LA, Gordillo-Guerrero A, Guidetti M, Maiorano A, Mantovani F, Marinari E, Martin-Mayor V, Munoz-Sudupe A, Navarro D, Parisi G, Perez-Gaviro S, Rossi M, Ruiz-Lorenzo JJ, Schifano SF, Sciretti D, Tarancon A, Tripiccione R, Velasco JL, Yllanes D, Zanier G. Janus: An FPGA-Based System for High-Performance Scientific Computing. Comput Sci Eng 2009. [DOI: 10.1109/mcse.2009.11] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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3
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Yin JQ, Zheng B, Trimper S. Dynamic Monte Carlo simulations of the three-dimensional random-bond Potts model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:036122. [PMID: 16241530 DOI: 10.1103/physreve.72.036122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2005] [Revised: 05/27/2005] [Indexed: 05/05/2023]
Abstract
The effect of random bonds on the phase transitions of the three-dimensional three-state Potts model is investigated with extensive dynamic Monte Carlo simulations. In the weakly disordered regime, the phase diagram is obtained with a recently suggested nonequilibrium reweighting method. The tricritical point separating the first- and second-order transitions is determined, and the critical exponents of the continuous phase transition induced by quenched randomness are estimated.
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Affiliation(s)
- J Q Yin
- Zhejiang University, Zhejiang Institute of Modern Physics, Hangzhou 310027, China
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Yin JQ, Zheng B, Trimper S. Critical behavior of the two-dimensional random-bond Potts model: a short-time dynamic approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:056134. [PMID: 15600719 DOI: 10.1103/physreve.70.056134] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2004] [Indexed: 05/24/2023]
Abstract
The short-time critical dynamics of the two-dimensional eight-state random-bond Potts model is investigated with large-scale Monte Carlo simulations. Dynamic relaxation starting from a disordered and an ordered state is carefully analyzed. The continuous phase transition induced by disorder is studied, and both the dynamic and static critical exponents are estimated. The static exponent beta/nu shows little dependence on the disorder amplitude r, while the dynamic exponent z and static exponent 1/nu vary with the strength of disorder.
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Affiliation(s)
- J Q Yin
- Zhejiang University, Zhejiang Institute of Modern Physics, Hangzhou 310027, China
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5
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Chatelain C, Berche B, Janke W, Berche PE. Softening of first-order transition in three-dimensions by quenched disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:036120. [PMID: 11580407 DOI: 10.1103/physreve.64.036120] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2000] [Indexed: 05/23/2023]
Abstract
We study by extensive Monte Carlo simulations the effect of random bond dilution on the phase transition of the three-dimensional four-state Potts model that is known to exhibit a strong first-order transition in the pure case. The phase diagram in the dilution-temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes. In the strongly disordered regime, numerical evidence for softening to a second-order transition induced by randomness is given. Here a large-scale finite-size scaling analysis, made difficult due to strong crossover effects presumably caused by the percolation fixed point, is performed.
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Affiliation(s)
- C Chatelain
- Laboratoire de Physique des Matériaux, Université Henri Poincaré, Nancy 1, Boîte Postal 239, F-54506 Vandoeuvre les Nancy Cedex, France
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Ying HP, Harada K. Short-time dynamics and magnetic critical behavior of the two-dimensional random-bond potts model. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:174-178. [PMID: 11088449 DOI: 10.1103/physreve.62.174] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2000] [Indexed: 05/23/2023]
Abstract
The critical behavior in the short-time dynamics for the random-bond Potts ferromagnet in two dimensions is investigated by short-time dynamic Monte Carlo simulations. The numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic, which is used to estimate the critical exponents straight theta,beta/nu, and z, for quenched disordered systems from the power-law behavior of the kth moments of magnetization.
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Affiliation(s)
- HP Ying
- Center for Computational Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan, and Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
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Chatelain C, Berche B. Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:3853-65. [PMID: 11970220 DOI: 10.1103/physreve.60.3853] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/1999] [Revised: 03/25/1999] [Indexed: 04/18/2023]
Abstract
We present a numerical study of two-dimensional random-bond Potts ferromagnets. The model is studied both below and above the critical value Qc=4, which discriminates between second- and first-order transitions in the pure system. Two geometries are considered, namely cylinders and square-shaped systems, and the critical behavior is investigated through conformal invariance techniques that were recently shown to be valid, even in the randomness-induced second-order phase transition regime Q>4. In the cylinder geometry, connectivity transfer matrix calculations provide a simple test to find the range of disorder amplitudes that is characteristic of the disordered fixed point. The scaling dimensions then follow from the exponential decay of correlations along the strip. Monte Carlo simulations of spin systems on the other hand are generally performed on systems of rectangular shape on the square lattice, but the data are then perturbed by strong surface effects. The conformal mapping of a semi-infinite system inside a square enables us to take into account boundary effects explicitly and leads to an accurate determination of the scaling dimensions. The techniques are applied to different values of Q in the range 3-64.
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Affiliation(s)
- C Chatelain
- Laboratoire de Physique des Matériaux, Université Henri Poincaré, Nancy 1, Boîte Postale 239, F-54506 Vandaeuvre les Nancy Cedex, France
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Paredes V R, Valbuena J. Effects of quenched disorder in the two-dimensional Potts model: a Monte Carlo study. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 59:6275-80. [PMID: 11969611 DOI: 10.1103/physreve.59.6275] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/1998] [Indexed: 04/18/2023]
Abstract
Motivated by recent experiments on phase behavior of systems confined in porous media, we have studied the effect of randomness on the nature of the phase transition in the two-dimensional Potts model. To model the effects of the porous matrix we introduce a random distribution of couplings P(J(ij))=pdelta(J(ij)-J1)+(1-p)delta(J(ij)-J2) in the q state Potts Hamiltonian. An extensive Monte Carlo study is made on this system for q=5. We studied two different cases of disorder (a) J(1)/J(2)-->infinity and p=0.8 and (b) J(1)/J(2)=10 and p=0.5. We observed, in both cases, that the weak first order transition that appears in the pure case, changes to a second-order transition. A finite size scaling analysis shows that the correlation length exponent nu is close to 1 and the best fit to the dependence of the specific heat on system size is logarithmic. This suggests that both cases belong to the universality class of the Ising model. In contrast, the magnetic exponents point to a different universality class.
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Affiliation(s)
- R Paredes V
- Laboratorio de Física Estadística de Sistemas Desordenados, Centro de Física, IVIC, Apartado 21827, Caracas 1020A, Venezuela
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Jug G, Shalaev BN. Critical behavior of weakly disordered anisotropic systems in two dimensions. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:3442-3453. [PMID: 9986245 DOI: 10.1103/physrevb.54.3442] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Budde K, Schwenger L, Voges C, Pfnür H. Effect of oxygen impurities on the critical properties of the (2 x 2)-2H/Ni(111) order-disorder phase transition. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:9275-9282. [PMID: 9979971 DOI: 10.1103/physrevb.52.9275] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sokolowski M, Pfnür H. Phase transitions of the striped domain-wall phases of S on Ru(0001). PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:15742-15751. [PMID: 9978551 DOI: 10.1103/physrevb.51.15742] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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