Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q

Abstract

We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of q. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.

RevTeX, 5 pages, includes 10 Postscript figures

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Cited by in corpus (14)

• Classifying Potts critical lines
• On superuniversality in the $q$-state Potts model with quenched disorder
• The three-state Potts antiferromagnet on plane quadrangulations
• Critical lines in the pure and disordered $O(N)$ model
• Particles, conformal invariance and criticality in pure and disordered systems
• On the phase diagram of the random bond $q$-state Potts model
• A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model
• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations
• The three-state Potts model on the centered triangular lattice
• From hard spheres to hard-core spins
• On zero-free regions for the anti-ferromagnetic Potts model on bounded-degree graphs
• Three lectures on random proper colorings of ${\mathbb{Z}}^d$
• Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus