Representation and poly-time approximation for pressure of ${\mathbb{Z}}^2$ lattice models in the non-uniqueness region

Abstract

We develop a new pressure representation theorem for nearest-neighbour Gibbs interactions and apply this to obtain the existence of efficient algorithms for approximating the pressure in the $2$-dimensional ferromagnetic Potts, multi-type Widom-Rowlinson and hard-core models. For Potts, our results apply to every inverse temperature but the critical. For Widom-Rowlinson and hard-core, they apply to certain subsets of both the subcritical and supercritical regions. The main novelty of our work is in the latter.

37 pages, 2 figures

References in corpus (1)

• On the Gibbs states of the noncritical Potts model on Z^2

Cited by in corpus (1)

• Algorithmic Pirogov-Sinai theory