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

Communications in Theoretical Physics

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

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

Published Dec 1, 1992• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/18/4/451

Related papers

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

Mean-field analysis of antiferromagnetic three-state Potts model with next-nearest-neighbor interaction

Mitsuhiro Itakura

The three-state Potts model with antiferromagnetic nearest-neighbor (NN) and ferromagnetic next-nearest-neighbor (NNN) interaction is investigated within a mean-field theory. We find that the phase diagram contains two kinds of ordered phases, the so-called broken-sublattice-symmetry and permutationally-symmetric-sublattice phases, separated by a discontinuous phase transition line. The order-disorder transition is continuous for weak NNN interactions and becomes a discontinuous transition, via a tricritical point, when the strength of the NNN interaction is increased.

arXiv:cond-mat/9605148•Physical review. B, Condensed matter•Jan 1, 1997•5 citations

Monte Carlo Study of the Antiferromagnetic Potts Model in Two Dimensions

Gary S. Grest, Jayanth R. Banavar

Results of Monte Carlo studies of the $q$-state Potts model on a square lattice with antiferromagnetic nearest-neighbor coupling and ferromagnetic next-nearest-neighbor coupling are presented for $q>~3$. The three-state Potts model shows a variety of unusual transitions whereas for $q>~4$, we find two first-order phase transitions separated by a broken sublattice symmetry state.

Physical Review Letters•Jun 1, 1981•52 citations

Z(3) criticality in three dimensions: Study of extended Potts models

Rajiv V. Gavai, F. Karsch

We investigate numerically the three-dimensional three-state Potts models with nearest-neighbor (NN) ferromagnetic coupling and next-nearest-neighbor (NNN) antiferromagnetic coupling of relative strength \ensuremath{\gamma} on ${\mathit{L}}^{3}$ lattices with L=12, 16, 20, 32, and 40. For all the \ensuremath{\gamma} values that we studied, 0.0\ensuremath{\le}\ensuremath{\gamma}\ensuremath{\le}0.8, we find indications of a first-order phase transition between the ordered and disordered phases. In the neighborhood of \ensuremath{\gamma}=0.25, the latent heat becomes rather small, making it necessary to use still larger lattices to rule out a higher-order phase transition at \ensuremath{\gamma}=0.25. We also studied the boundary regimes of the three different ordered phases and find no criticality along them, thus suggesting a lack of criticality in these extended Potts models.

Physical review. B, Condensed matter•Jul 1, 1992•7 citations

An Analytical Study of Three-State Potts Model on Lattice

Zhao Peiying, Wu Ji-Min

We investigate the phase structure of the three-state Potts model by the variational cumulant expansion approach. It is shown that there is a weak first-order phase transition in three and four dimensions. The critical coupling given by this method is in good agreement with MC data.

Communications in Theoretical Physics•May 1, 2006•0 citations

An Analytical Study of Three-State Potts Model on Lattice

赵佩英, 吴济民

We investigate the phase structure of the three-state Potts model by the variational cumulant expansion approach. It is shown that there is a weak first-order phase transition in three and four dimensions. The critical coupling given by this method is in good agreement with MC data.

•Jan 1, 2006•0 citations
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.
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.
The three-state Potts model with antiferromagnetic nearest-neighbor (NN) and ferromagnetic next-nearest-neighbor (NNN) interaction is investigated within a mean-field theory. We find that the phase diagram contains two kinds of ordered phases, the so-called broken-sublattice-symmetry and permutationally-symmetric-sublattice phases, separated by a discontinuous phase transition line. The order-disorder transition is continuous for weak NNN interactions and becomes a discontinuous transition, via a tricritical point, when the strength of the NNN interaction is increased.
Results of Monte Carlo studies of the qqq-state Potts model on a square lattice with antiferromagnetic nearest-neighbor coupling and ferromagnetic next-nearest-neighbor coupling are presented for q> 3q>~3q> 3. The three-state Potts model shows a variety of unusual transitions whereas for q> 4q>~4q> 4, we find two first-order phase transitions separated by a broken sublattice symmetry state.
We investigate numerically the three-dimensional three-state Potts models with nearest-neighbor (NN) ferromagnetic coupling and next-nearest-neighbor (NNN) antiferromagnetic coupling of relative strength \ensuremath{\gamma} on L3{\mathit{L}}^{3}L3 lattices with L=12, 16, 20, 32, and 40. For all the \ensuremath{\gamma} values that we studied, 0.0\ensuremath{\le}\ensuremath{\gamma}\ensuremath{\le}0.8, we find indications of a first-order phase transition between the ordered and disordered phases. In the neighborhood of \ensuremath{\gamma}=0.25, the latent heat becomes rather small, making it necessary to use still larger lattices to rule out a higher-order phase transition at \ensuremath{\gamma}=0.25. We also studied the boundary regimes of the three different ordered phases and find no criticality along them, thus suggesting a lack of criticality in these extended Potts models.