  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.
