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

arXiv:cond-mat/0606225 · Journal of Physics A Mathematical and General

Monte Carlo study of the antiferromagnetic three-state Potts model with a staggered polarization field on the square lattice

Yutaka Okabe, Hiromi Otsuka

Published Jul 5, 2006• 10 citations
arXivHTMLPDF

Abstract

Using the Wang–Landau Monte Carlo method, we study the antiferromagnetic (AF) three-state Potts model with a staggered polarization field on the square lattice. We obtain two phase transitions: one belongs to the ferromagnetic three-state Potts universality class and the other to the Ising universality class. The phase diagram obtained is quantitatively consistent with the transfer matrix calculation. The Ising transition in the large nearest-neighbour interaction limit has been made clear by the detailed analysis of the energy density of states.

DOI
10.1088/0305-4470/39/29/006

Related papers

Phase Diagram of the Square-Lattice Three-State Potts Antiferromagnet with a Staggered Polarization Field

Hiromi Otsuka, Yutaka Okabe

We study a square-lattice three-state Potts antiferromagnet with a staggered polarization field at finite temperature. Numerically treating the transfer matrices, we determine two phase boundaries separating the model-parameter space into three parts. We confirm that one of them belongs to the ferromagnetic three-state Potts criticality, which is in accord with a recent prediction, and another to the Ising-type; these are both corresponding to the massless renormalization-group flows stemming from the Gaussian fixed points. We also discuss a field theory to describe the latter Ising transition.

arXiv:cond-mat/0408444•Physical Review Letters•Sep 14, 2004•9 citations

Monte Carlo simulation of quantum Potts model

Chengxiang Ding, Yangcheng Wang, Youjin Deng +1 more

Using Monte Carlo simulations in the frame of stochastic series expansion (SSE), we study the three-state quantum Potts model. The cluster algorithm we used is a direct generalization of that for the quantum Ising model. The simulations include the one dimensional and two dimensional ferromagnetic three-state quantum Potts model and the two dimensional antiferromagnetic three-state quantum Potts model. Our results show that the phase transition of the one dimensional ferromagnetic quantum Potts model belongs to the same universality class of the two dimensional classical Potts model, the two dimensional ferromagnetic quantum Potts model undergoes a first order transition, which is also in analogy to its classical correspondence. The phase transition of the antiferromagnetic quantum Potts model is continuous, whose universality class belongs to the three-dimensional classical XY model, owing to an `emergent' O(2) symmetry at the critical point, although its ordered phase breaks the Z_6 symmetry.

arXiv:1702.02675•Feb 9, 2017•3 citations

Three-state Potts model on the maple leaf lattice

Z. F. Wang, B. W. Southern

We use Monte Carlo methods to study the three-state Potts model on a two-dimensional lattice with fivefold coordination. The lattice consists of triangular and hexagonal units and has properties intermediate between the triangular and kagom\'e lattices. The critical behavior of both ferromagnetic and antiferromagnetic cases is considered. As expected, the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. A critical end point is found at the coexistence between the ferromagnetic and antiferromagnetic phases, and the transition to the antiferromagnetic state is always first order.

Physical review. B, Condensed matter•Sep 18, 2003•7 citations

Three-state Potts model on the centered triangular lattice

Zhe Fu, Wenan Guo, Henk W. J. Blöte

We study phase transitions of the Potts model on the centered-triangular lattice with two types of couplings, namely, K between neighboring triangular sites, and J between the centered and the triangular sites. Results are obtained by means of a finite-size analysis based on numerical transfer-matrix calculations and Monte Carlo simulations. Our investigation covers the whole (K,J) phase diagram, but we find that most of the interesting physics applies to the antiferromagnetic case K<0, where the model is geometrically frustrated. In particular, we find that there are, for all finite J, two transitions when K is varied. Their critical properties are explored. In the limits J→±∞ we find algebraic phases with infinite-order transitions to the ferromagnetic phase.

arXiv:1909.04979•Physical review. E•Jan 14, 2020•5 citations

A first-order phase transition in the three-dimensional four-state antiferromagnetic Potts model

A Yamagata

Studies the four-state antiferromagnetic Potts model with next-nearest-neighbour ferromagnetic interactions on the simple cubic lattice by the Monte Carlo method. The ratio J 2 /J 1 of the strength of the next-nearest-neighbour interactions to that of the nearest-neighbour interactions is to be 10. The author analyses the finite-size effects of the energy, the specific heat, the fourth-order cumulant, the magnetization, the susceptibility and the effective transition temperatures. With the help of the finite-size scaling theory the author concludes that the transition of the model is assigned to be of first order.

Journal of Physics A Mathematical and General•Feb 7, 1993•5 citations

Critical Properties of Antiferromagnetic Potts Model on a bcc Lattice

Djuma R. Kurbanova, A. K. Murtazaev, М. А. Магомедов +2 more

Abstract The Monte Carlo method has been used to study phase transitions and critical properties of the antiferromagnetic 3-state Potts model on a body-centered cubic lattice with interactions of the first (J1) and second (J2) nearest neighbors. The competition of exchange interactions in the range –2/3 < J2 < 0 was determined to result in a phase separation. In the low-temperature region, an ordered phase, lying inside the phase with broken sublattice symmetry, was found. The magnetic structures of the ground state corresponding to different regions of the phase diagram have been obtained. The analysis of the phase transition order has been carried out using the Binder cumulant method and the histogram method. It has been revealed that the interaction of the second nearest neighbors leads to a change in the type of phase transition. Static critical exponents have been calculated based on scaling relations. The critical exponents correspond to the universality class of the three-dimensional XY model.

The Physics of Metals and Metallography•Dec 1, 2025•0 citations
Using the Wang–Landau Monte Carlo method, we study the antiferromagnetic (AF) three-state Potts model with a staggered polarization field on the square lattice. We obtain two phase transitions: one belongs to the ferromagnetic three-state Potts universality class and the other to the Ising universality class. The phase diagram obtained is quantitatively consistent with the transfer matrix calculation. The Ising transition in the large nearest-neighbour interaction limit has been made clear by the detailed analysis of the energy density of states.
We study a square-lattice three-state Potts antiferromagnet with a staggered polarization field at finite temperature. Numerically treating the transfer matrices, we determine two phase boundaries separating the model-parameter space into three parts. We confirm that one of them belongs to the ferromagnetic three-state Potts criticality, which is in accord with a recent prediction, and another to the Ising-type; these are both corresponding to the massless renormalization-group flows stemming from the Gaussian fixed points. We also discuss a field theory to describe the latter Ising transition.
Using Monte Carlo simulations in the frame of stochastic series expansion (SSE), we study the three-state quantum Potts model. The cluster algorithm we used is a direct generalization of that for the quantum Ising model. The simulations include the one dimensional and two dimensional ferromagnetic three-state quantum Potts model and the two dimensional antiferromagnetic three-state quantum Potts model. Our results show that the phase transition of the one dimensional ferromagnetic quantum Potts model belongs to the same universality class of the two dimensional classical Potts model, the two dimensional ferromagnetic quantum Potts model undergoes a first order transition, which is also in analogy to its classical correspondence. The phase transition of the antiferromagnetic quantum Potts model is continuous, whose universality class belongs to the three-dimensional classical XY model, owing to an `emergent' O(2) symmetry at the critical point, although its ordered phase breaks the Z_6 symmetry.
We use Monte Carlo methods to study the three-state Potts model on a two-dimensional lattice with fivefold coordination. The lattice consists of triangular and hexagonal units and has properties intermediate between the triangular and kagom\'e lattices. The critical behavior of both ferromagnetic and antiferromagnetic cases is considered. As expected, the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. A critical end point is found at the coexistence between the ferromagnetic and antiferromagnetic phases, and the transition to the antiferromagnetic state is always first order.
We study phase transitions of the Potts model on the centered-triangular lattice with two types of couplings, namely, K between neighboring triangular sites, and J between the centered and the triangular sites. Results are obtained by means of a finite-size analysis based on numerical transfer-matrix calculations and Monte Carlo simulations. Our investigation covers the whole (K,J) phase diagram, but we find that most of the interesting physics applies to the antiferromagnetic case K<0, where the model is geometrically frustrated. In particular, we find that there are, for all finite J, two transitions when K is varied. Their critical properties are explored. In the limits J→±∞ we find algebraic phases with infinite-order transitions to the ferromagnetic phase.
Studies the four-state antiferromagnetic Potts model with next-nearest-neighbour ferromagnetic interactions on the simple cubic lattice by the Monte Carlo method. The ratio J 2 /J 1 of the strength of the next-nearest-neighbour interactions to that of the nearest-neighbour interactions is to be 10. The author analyses the finite-size effects of the energy, the specific heat, the fourth-order cumulant, the magnetization, the susceptibility and the effective transition temperatures. With the help of the finite-size scaling theory the author concludes that the transition of the model is assigned to be of first order.
Abstract The Monte Carlo method has been used to study phase transitions and critical properties of the antiferromagnetic 3-state Potts model on a body-centered cubic lattice with interactions of the first (J1) and second (J2) nearest neighbors. The competition of exchange interactions in the range –2/3 < J2 < 0 was determined to result in a phase separation. In the low-temperature region, an ordered phase, lying inside the phase with broken sublattice symmetry, was found. The magnetic structures of the ground state corresponding to different regions of the phase diagram have been obtained. The analysis of the phase transition order has been carried out using the Binder cumulant method and the histogram method. It has been revealed that the interaction of the second nearest neighbors leads to a change in the type of phase transition. Static critical exponents have been calculated based on scaling relations. The critical exponents correspond to the universality class of the three-dimensional XY model.