The Potts model built on sand

TL;DR

This paper studies a modified 4-state Potts model on a square lattice with a nonlocal interaction derived from the abelian sandpile model, revealing a stable phase with exponential decay of correlations at low temperatures.

Contribution

It introduces a new nonlocal interaction in the Potts model based on sandpile configurations and analyzes its phase diagram, demonstrating a stable phase with exponential decay.

Findings

Existence of a single stable phase at low temperatures

Correlation functions decay exponentially in the stable phase

Density of the state '4' approaches one as temperature approaches zero

Abstract

We consider the q=4 Potts model on the square lattice with an additional hard-core nonlocal interaction. That interaction arises from the choice of the reference measure taken to be the uniform measure on the recurrent configurations for the abelian sandpile model. In that reference measure some correlation functions have a power-law decay. We investigate the low-temperature phase diagram and we prove the existence of a single stable phase with exponential decay of correlations. For all boundary conditions the density of 4 in the infinite volume limit goes to one as the temperature tends to zero.