E. Dinaburg, C. Maes, S. Pirogov, F. Redig and A. Rybko
The Potts model built on sand
(277K, pdf)

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.