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 Physics A Mathematical and General

The ferro/antiferromagneticq-state Potts model

Damien Paul Foster, C Gérard

Published Feb 11, 2002• 8 citations
Publisher

Abstract

The critical properties of the mixed ferro/antiferromagnetic q -state Potts model on the square lattice are investigated using the numerical transfer matrix technique. The transition temperature is found to be substantially lower than previously found for q = 3. It is conjectured that there is no transition for q >3, in contradiction with previous results.

DOI
10.1088/0305-4470/35/7/101

Related papers

The ferro/antiferromagnetic q-state Potts model

Damien Paul Foster, C Gérard

The critical properties of the mixed ferro/antiferromagnetic q-state Potts model on the square lattice are investigated using the numerical transfer matrix technique. The transition temperature is found to be substantially lower than previously found for q=3. It is conjectured that there is no transition for q>3, in contradiction with previous results.

arXiv:cond-mat/0201383•Jan 22, 2002•2 citations

Critical behaviour of the three-state antiferromagnetic Potts model in two dimensions

P Reed

The critical properties of the three-state Potts antiferromagnet on a square lattice have been investigated by 'large-cell' renormalisation using an exact numerical technique. The results indicate the existence of a single fixed point at beta -1=0.

Journal of Physics C Solid State Physics•Oct 10, 1985•1 citation

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

Kosterlitz Thouless transition in three-state mixed Potts ferro antiferromagnets

Miguel Quartin, S. L. A. de Queiroz

We study three-state Potts spins on a square lattice, in which all bonds are ferromagnetic along one of the lattice directions, and antiferromagnetic along the other. Numerical transfer-matrix methods are used on infinite strips of width L sites, 4 ⩽ L ⩽ 14. Based on the analysis of the ratio of scaled mass gaps (inverse correlation lengths) and scaled domain-wall free energies, we provide strong evidence that a critical (Kosterlitz–Thouless) phase is present, whose upper limit is, in our best estimate, T c = 0.29 ± 0.01. From an analysis of the (extremely anisotropic) nature of excitations below T c , we argue that the critical phase extends all the way down to T = 0. While domain walls parallel to the ferromagnetic direction are soft for the whole extent of the critical phase, those along the antiferromagnetic direction seem to undergo a softening transition at a finite temperature. Assuming a bulk correlation length varying, for T > T c , as ξ( T ) = a ξ exp[ b ξ ( T − T c ) −σ ], σ ≃ 1/2, we attempt finite-size scaling plots of our finite-width correlation lengths. Our best results are for T c = 0.50 ± 0.01. We propose a scenario in which such inconsistency is attributed to the extreme narrowness of the critical region.

arXiv:cond-mat/0209415•Journal of Physics A Mathematical and General•Jan 15, 2003•7 citations

Three-state square lattice Potts antiferromagnet

M. P. Nightingale, Michael Schick C

The three state antiferromagnetic Potts model on a square lattice is investigated via phenomenological renormalisation group methods. In contrast to previous calculations, the results indicate that there exists neither an ordered phase nor a massless phase with algebraic decay of correlations. The sole critical point is at zero temperature, where an essential singularity is found.

Journal of Physics A Mathematical and General•Jan 1, 1982•55 citations

Critical behaviour of a (1+1) dimensional Potts model with ferromagnetic and antiferromagnetic interactions

Hans Jürgen Herrmann, H. O. Mártin

The authors study the one-dimensional quantum Hamiltonian version of a two-dimensional three-state Potts model on a square lattice which has ferromagnetic interactions in the x direction and antiferromagnetic interactions in the y direction in the limit of strong coupling in the x direction. They find a massless low-temperature behaviour. The transition point which has an essential singularity is located at a different point as previously conjectured.

Journal of Physics A Mathematical and General•Feb 21, 1984•14 citations
The critical properties of the mixed ferro/antiferromagnetic q -state Potts model on the square lattice are investigated using the numerical transfer matrix technique. The transition temperature is found to be substantially lower than previously found for q = 3. It is conjectured that there is no transition for q >3, in contradiction with previous results.
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.
We study three-state Potts spins on a square lattice, in which all bonds are ferromagnetic along one of the lattice directions, and antiferromagnetic along the other. Numerical transfer-matrix methods are used on infinite strips of width L sites, 4 ⩽ L ⩽ 14. Based on the analysis of the ratio of scaled mass gaps (inverse correlation lengths) and scaled domain-wall free energies, we provide strong evidence that a critical (Kosterlitz–Thouless) phase is present, whose upper limit is, in our best estimate, T c = 0.29 ± 0.01. From an analysis of the (extremely anisotropic) nature of excitations below T c , we argue that the critical phase extends all the way down to T = 0. While domain walls parallel to the ferromagnetic direction are soft for the whole extent of the critical phase, those along the antiferromagnetic direction seem to undergo a softening transition at a finite temperature. Assuming a bulk correlation length varying, for T > T c , as ξ( T ) = a ξ exp[ b ξ ( T − T c ) −σ ], σ ≃ 1/2, we attempt finite-size scaling plots of our finite-width correlation lengths. Our best results are for T c = 0.50 ± 0.01. We propose a scenario in which such inconsistency is attributed to the extreme narrowness of the critical region.