The Potts model built on sand
Statistical Mechanics
2015-05-26 v1 Soft Condensed Matter
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.
Cite
@article{arxiv.cond-mat/0312363,
title = {The Potts model built on sand},
author = {E. Dinaburg and C. Maes and S. Pirogov and F. Redig and A. Rybko},
journal= {arXiv preprint arXiv:cond-mat/0312363},
year = {2015}
}