Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations

Abstract

We provide a new criterion based on graph duality to predict whether the 3-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge $c=1$. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the 3-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

6 pages, LaTeX2e. Contains 4 postscript figures. Uses revtex4-1. Final journal version

References in corpus (3)

• Phase transition in the 3-state Potts antiferromagnet on the diced lattice
• Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
• The three-state Potts antiferromagnet on plane quadrangulations

Cited by in corpus (4)

• The three-state Potts antiferromagnet on plane quadrangulations
• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus
• Crystal chemistry criteria of the existence of spin liquids on the kagome lattice