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

Physical review. B, Condensed matter

Monte Carlo renormalization-group analysis of the antiferromagnetic three-state Potts model on a square lattice

Ciriyam Jayaprakash, Jan Tobochnik

Published Apr 1, 1982• 26 citations
Publisher

Abstract

Monte Carlo renormalization-group calculations have been performed on the three-state anti-ferromagnetic Potts model on a square lattice. The results are consistent with the conclusion that there is no transition as a function of temperature.
DOI
10.1103/physrevb.25.4890

Related papers

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

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

Yutaka Okabe, Hiromi Otsuka

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.

arXiv:cond-mat/0606225•Journal of Physics A Mathematical and General•Jul 5, 2006•10 citations

A Monte Carlo study of the three-states antiferromagnetic Potts model in two dimensions

Francesco Fucito

Using Monte Carlo methods the author studies the two-dimensional three-stages Potts model with antiferromagnetic nearest neighbours and ferromagnetic next-nearest neighbours couplings on a square lattice. The author focuses on the case with only antiferromagnetic coupling; from the analysis of the data gathered, there is evidence that this system shows critical behaviour only at T=0.

Journal of Physics A Mathematical and General•Oct 1, 1983•8 citations

Three-state Potts model with antiferromagnetic interactions: a MFRG approach

M C Marques

The mean-field renormalisation group method is used to study the critical temperature of the three-state Potts antiferromagnet in 3D lattices, as well as the three-state Potts model on the square lattice with ferromagnetic (along x) and antiferromagnetic (along y) interactions, and its quantum version, the 1D Potts antiferromagnet in a transverse field. Comparison is made with other results.

Journal of Physics A Mathematical and General•Feb 21, 1988•15 citations

Antiferromagnetic Potts and Ashkin-Teller models in three dimensions

Jayanth R. Banavar, Gary S. Grest, David Jasnow

Monte Carlo simulations and renormalization-group ideas are used to analyze the behavior of the antiferromagnetic Potts model and the Ashkin-Teller model in three dimensions. A variety of continuous transitions, observed in the Monte Carlo data on the antiferromagnetic Potts model for simple cubic and body-centered-cubic lattices, are found to be consistent with $\ensuremath{\epsilon}$-expansion analyses of these models. A glassy "plastic crystal" phase is observed, along with the analog of the glass transition in the four-state antiferromagnetic Potts model. An $\ensuremath{\epsilon}$-expansion analysis of the Ashkin-Teller model is found to yield results consistent with those obtained by Ditzian et al. using series analysis and Monte Carlo simulations.

Physical review. B, Condensed matter•Apr 1, 1982•66 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
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.
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.
Monte Carlo simulations and renormalization-group ideas are used to analyze the behavior of the antiferromagnetic Potts model and the Ashkin-Teller model in three dimensions. A variety of continuous transitions, observed in the Monte Carlo data on the antiferromagnetic Potts model for simple cubic and body-centered-cubic lattices, are found to be consistent with $\ensuremath{\epsilon}$-expansion analyses of these models. A glassy "plastic crystal" phase is observed, along with the analog of the glass transition in the four-state antiferromagnetic Potts model. An $\ensuremath{\epsilon}$-expansion analysis of the Ashkin-Teller model is found to yield results consistent with those obtained by Ditzian et al. using series analysis and Monte Carlo simulations.