Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Modern Physics Letters B

IMPORTANCE-SAMPLING MONTE CARLO METHOD AND ENTROPY OF q-STATE POTTS MODEL

Hsing-Mei Huang

Published Aug 10, 1992• 0 citations
Publisher

Abstract

An importance-sampling Monte Carlo method is applied to the calculation of Γ(E), the number of states for a given energy E, and Γ(E, S), the number of states for given energy E and spin S, of antiferromagnetic two-dimensional q=2,3,4,5,6 Potts models. The entropy function is derived for various temperatures, and our results for the q=3 model show a continuous phase transition.

DOI
10.1142/s0217984992001988

Related papers

FINITE TEMPERATURE ENTROPY OF THE ANTIFERROMAGNETIC POTTS MODEL

X. Y. CHEN, C. Y. Pan

Monte Carlo simulation is used to deal with the finite temperature entropy of the q-state antiferromagnetic Potts model which is the extension of the general q-color problem (at zero temperature). The finite temperature entropy of the model in two and three dimensions is obtained which is consistent with the zero temperature results. A possible universal relation of the model to determine when the order-disorder transition happens is proposed.

International Journal of Modern Physics B•Dec 1, 1988•2 citations

Three-dimensional antiferromagneticq-state Potts models: application of the Wang-Landau algorithm

Chiaki Yamaguchi, Yutaka Okabe

We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q -state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with q = 3, 4, 5 and 6. We obtain the finite-temperature phase transition for q = 3 and 4, whereas the transition temperature is down to zero for q = 5. For q = 6 there exists no order for any temperature. We also study the ground-state properties. The size dependence of the ground-state entropy is investigated. We find that the ground-state entropy is larger than the contribution from the typical configurations of the broken-sublattice-symmetry state for q = 3. The same situations are found for q = 4, 5 and 6.

arXiv:cond-mat/0108540•Journal of Physics A Mathematical and General•Oct 15, 2001•82 citations

Monte Carlo study of the phase transitions in 2D ferro- and antiferromagnetic Potts models on a triangular lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

The phase transitions in 2D ferro- and antiferromagnetic Potts models with number of spin states q = 3 on a triangular lattice are investigated by the cluster and classical Monte Carlo methods. Systems with linear sizes L = 20–120 are considered. Fourth-order Binder cumulants and histogram data analysis are used to show that second- and first-order phase transitions are observed in the ferromagnetic and antiferromagnetic Potts models, respectively. The static critical indices are calculated for specific heat α, susceptibility γ, magnetization β, and correlation length ν on the basis of finite-size scaling theory for a ferromagnetic Potts model.

Bulletin of the Russian Academy of Sciences Physics•Jan 1, 2014•2 citations

Phase transitions in the two-dimensional ferro- and antiferromagnetic potts models on a triangular lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.

Journal of Experimental and Theoretical Physics•Dec 1, 2012•17 citations

DENSITY-OF-STATES MONTE CARLO METHOD FOR SIMULATION OF TWO-DIMENSIONAL RANDOM BOND POTTS MODEL

You Yu, He-Ping Ying, Qing‐Hu Chen +1 more

Softening of the phase transition and critical phenomena for the 2D random-bond Potts ferromagnet is investigated by using the density-of-states Monte Carlo method to calculate the thermodynamic properties with a variety of the quenched bond-randomness characterized by a disorder amplitude r=Ks/Kw. The numerical results show that the crossover from the 1st- to 2nd-order transition was induced at finite lattices for the self-dual bimodal distribution.

International Journal of Modern Physics B•Jul 30, 2004•0 citations

Cluster Monte Carlo study of the antiferromagnetic Z(q) model

A. Benyoussef, Mohamed Loulidi, Abdeljalil Rachadi

A cluster Monte Carlo (MC) updating algorithm is presented for the antiferromagnetic $Z(q)$ model, into which Ising variables are embedded. Using MC simulations combined with the histogram technique, we were able to study the q-state clock model, for $q=5$ and $q=7,$ in $d=2$ and $d=3$ dimensions. The two-dimensional system exhibits a phase transition at temperature $T=0$ for both $q=5$ and $q=7$ system states. The critical exponents were derived as well as the ground state entropy for $T=0.$ Our results for the $q=5$ and the $q=7$ three-dimensional systems show that they exhibit a phase transition at nonzero temperature.

Physical review. B, Condensed matter•Mar 20, 2003•2 citations
An importance-sampling Monte Carlo method is applied to the calculation of Γ(E), the number of states for a given energy E, and Γ(E, S), the number of states for given energy E and spin S, of antiferromagnetic two-dimensional q=2,3,4,5,6 Potts models. The entropy function is derived for various temperatures, and our results for the q=3 model show a continuous phase transition.
We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q -state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with q = 3, 4, 5 and 6. We obtain the finite-temperature phase transition for q = 3 and 4, whereas the transition temperature is down to zero for q = 5. For q = 6 there exists no order for any temperature. We also study the ground-state properties. The size dependence of the ground-state entropy is investigated. We find that the ground-state entropy is larger than the contribution from the typical configurations of the broken-sublattice-symmetry state for q = 3. The same situations are found for q = 4, 5 and 6.
The phase transitions in 2D ferro- and antiferromagnetic Potts models with number of spin states q = 3 on a triangular lattice are investigated by the cluster and classical Monte Carlo methods. Systems with linear sizes L = 20–120 are considered. Fourth-order Binder cumulants and histogram data analysis are used to show that second- and first-order phase transitions are observed in the ferromagnetic and antiferromagnetic Potts models, respectively. The static critical indices are calculated for specific heat α, susceptibility γ, magnetization β, and correlation length ν on the basis of finite-size scaling theory for a ferromagnetic Potts model.
The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.
A cluster Monte Carlo (MC) updating algorithm is presented for the antiferromagnetic Z(q)Z(q)Z(q) model, into which Ising variables are embedded. Using MC simulations combined with the histogram technique, we were able to study the q-state clock model, for q=5q=5q=5 and q=7,q=7,q=7, in d=2d=2d=2 and d=3d=3d=3 dimensions. The two-dimensional system exhibits a phase transition at temperature T=0T=0T=0 for both q=5q=5q=5 and q=7q=7q=7 system states. The critical exponents were derived as well as the ground state entropy for T=0.T=0.T=0. Our results for the q=5q=5q=5 and the q=7q=7q=7 three-dimensional systems show that they exhibit a phase transition at nonzero temperature.