A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model

Abstract

We give a general condition for a discrete spin system with nearest-neighbor interactions on the ${\mathbb{Z}}^d$ lattice to exhibit long-range order. The condition is applicable to systems with residual entropy in which the long-range order is entropically driven. As a main example we consider the antiferromagnetic $q$-state Potts model and rigorously prove the existence of a broken sub-lattice symmetry phase at low temperature and high dimension -- a new result for $q\ge 4$. As further examples, we prove the existence of an ordered phase in a clock model with hard constraints and extend the known regime of the demixed phase in the lattice Widom-Rowlinson model.

6 pages, 1 figure. Revised introduction

References in corpus (4)

• Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem
• Ground State Entropy and the $q=3$ Potts Antiferromagnet on the Honeycomb Lattice
• Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
• Partial long-range order in antiferromagnetic Potts models

Cited by in corpus (4)

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