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

Journal of the Physical Society of Japan

Theory of Generalized 3-State Potts Model and Antiferromagnetic Potts Model

Takehiko Oguchi, Takuma Ishikawa, Haruo Yoshida

Published Mar 1, 1982• 7 citations
Publisher

Abstract

The spin Hamiltonian with spin-1 system including a single parameter is proposed which expresses the 3-state Potts model (PM) or antiferromagnetic Potts model (AFPM) according as a value of the parameter. They are investigated by a new method which is the extension of the effective Hamiltonian method in a unified way. The first-order transition or the second-order transition are obtained for the PM or the AFPM, respectively. In the AFPM, the ordered phase has a residual entropy, nevertheless the ordered phase can exist stably.

DOI
10.1143/jpsj.51.723

Related papers

Phase transitions in the three-state antiferromagnetic Potts model

Petras J. Kundrotas, Saulius Lapinskas, Anders Rosengren

The three-state antiferromagnetic Potts model on the simple cubic lattice is studied by the Monte Carlo method using a new order parameter and employing the histogram technique. It is shown that apart from the low-temperature broken-sublattice-symmetry phase with nonequivalent sublattices, another type of ordering with equivalent sublattices does exist in the model between the broken-sublattice-symmetry and disordered phases. The temperature of the transition between the ordered phases is estimated from the histogram of the order parameter. The value obtained is in good agreement with that obtained from cluster variation circulations.

Physical review. B, Condensed matter•Oct 1, 1995•13 citations

The Phase Transition in the Three-State Potts Model: An Analytical Analysis

Ya-Li Song, Jin Min Yang, Gong Ru Lu

We investigate the phase transition of the three-state Potts model in an analytical approach—the generalized cumulant expansion with the effective mean field hypothesis. We find a first order phase transition in the three-dimensional three-state Potts model with ferromagnetic nearest neighbor coupling. For the model with antiferromagnetic next-to-nearest neighbor coupling, we find a first order transition when the relative strength of the -coupling is fixed to . The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.

Communications in Theoretical Physics•Dec 1, 1992•0 citations

High Temperature Series Expansion of the d-Dimensional q-State Antiferromagnetic Potts Model

Kaoru Yasumura, Takehiko Oguchi

High temperature series expansions of the staggered susceptibility of the q -state antiferromagnetic Potts model (AFPM) on a d -dimensional hypercubic lattice are calculated. For arbitrary values of q and d , the transition temperatures and the critical exponents γ are determined by use of the ratio method and the Padé approximation. It is shown that the 3- and 4-state AFPM exhibit a second-order phase transition when d ≥3, and the 5- and 6-state AFPM do when d ≥4, etc. In the limit of infinite d , the transition temperature T c is obtained rigorously as k T c / J ={log [2 d /(2 d - q )]} -1 ( k : the Boltzmann constant, J : the interaction parameter), and the ordered phase exists when d > q /2.

Journal of the Physical Society of Japan•Feb 1, 1984•9 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

Critical properties of 2d disordered 3-state antiferromagnetic potts model ON TRIANGULAR LATTICE

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Ataeva

By introducing a small amount of non-magnetic impurities into an antiferromagnetic (AF) two-dimensional (2D) Potts model on a triangular lattice it is that the impurities in spin systems described by this model result in the change of a first order to a second-order phase transition. The systems with linear sizes L × L = N, L = 9-144 are considered. Investigations are performed using the standard Metropolis algorithm along with Monte-Carlo single-cluster Wolff algorithm. On the basis of the theory of finite-size scaling, critical exponents (CE) are calculated: the heat capacity α, the susceptibility γ, the order parameter β, and the CE of the correlation radius ν.

EPJ Web of Conferences•Jan 1, 2018•0 citations

Antiferromagnetic Potts Model on the Body-Centered Cubic Lattice

Djuma R. Kurbanova, Рамазанов Магомедшейх Курбанович, М. А. Магомедов +1 more

Abstract We have studied phase transitions and thermodynamic properties of the antiferromagnetic Potts model with number of spin states q = 3 on a body-centered cubic lattice by the Monte Carlo method. Investigations have been performed with account for exchange interactions J1 and J2 between the first and second nearest neighbors. The phase transition order has been analyzed using the histogram method. It is found that in this model with J2 = 0, a second-order phase transition is observed. It is concluded that the inclusion of the interaction between the second nearest neighbors changes the type of the phase transition.

Journal of Experimental and Theoretical Physics•Jun 1, 2023•4 citations
The spin Hamiltonian with spin-1 system including a single parameter is proposed which expresses the 3-state Potts model (PM) or antiferromagnetic Potts model (AFPM) according as a value of the parameter. They are investigated by a new method which is the extension of the effective Hamiltonian method in a unified way. The first-order transition or the second-order transition are obtained for the PM or the AFPM, respectively. In the AFPM, the ordered phase has a residual entropy, nevertheless the ordered phase can exist stably.
The three-state antiferromagnetic Potts model on the simple cubic lattice is studied by the Monte Carlo method using a new order parameter and employing the histogram technique. It is shown that apart from the low-temperature broken-sublattice-symmetry phase with nonequivalent sublattices, another type of ordering with equivalent sublattices does exist in the model between the broken-sublattice-symmetry and disordered phases. The temperature of the transition between the ordered phases is estimated from the histogram of the order parameter. The value obtained is in good agreement with that obtained from cluster variation circulations.
We investigate the phase transition of the three-state Potts model in an analytical approach—the generalized cumulant expansion with the effective mean field hypothesis. We find a first order phase transition in the three-dimensional three-state Potts model with ferromagnetic nearest neighbor coupling. For the model with antiferromagnetic next-to-nearest neighbor coupling, we find a first order transition when the relative strength of the -coupling is fixed to . The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.
High temperature series expansions of the staggered susceptibility of the q -state antiferromagnetic Potts model (AFPM) on a d -dimensional hypercubic lattice are calculated. For arbitrary values of q and d , the transition temperatures and the critical exponents γ are determined by use of the ratio method and the Padé approximation. It is shown that the 3- and 4-state AFPM exhibit a second-order phase transition when d ≥3, and the 5- and 6-state AFPM do when d ≥4, etc. In the limit of infinite d , the transition temperature T c is obtained rigorously as k T c / J ={log [2 d /(2 d - q )]} -1 ( k : the Boltzmann constant, J : the interaction parameter), and the ordered phase exists when d > q /2.
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.
By introducing a small amount of non-magnetic impurities into an antiferromagnetic (AF) two-dimensional (2D) Potts model on a triangular lattice it is that the impurities in spin systems described by this model result in the change of a first order to a second-order phase transition. The systems with linear sizes L × L = N, L = 9-144 are considered. Investigations are performed using the standard Metropolis algorithm along with Monte-Carlo single-cluster Wolff algorithm. On the basis of the theory of finite-size scaling, critical exponents (CE) are calculated: the heat capacity α, the susceptibility γ, the order parameter β, and the CE of the correlation radius ν.
Abstract We have studied phase transitions and thermodynamic properties of the antiferromagnetic Potts model with number of spin states q = 3 on a body-centered cubic lattice by the Monte Carlo method. Investigations have been performed with account for exchange interactions J1 and J2 between the first and second nearest neighbors. The phase transition order has been analyzed using the histogram method. It is found that in this model with J2 = 0, a second-order phase transition is observed. It is concluded that the inclusion of the interaction between the second nearest neighbors changes the type of the phase transition.