English

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

Dynamical Systems 2016-02-17 v1 Mathematical Physics math.MP Probability

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 22-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.

Keywords

Cite

@article{arxiv.1508.06590,
  title  = {Representation and poly-time approximation for pressure of $\mathbb{Z}^2$ lattice models in the non-uniqueness region},
  author = {Stefan Adams and Raimundo Briceño and Brian Marcus and Ronnie Pavlov},
  journal= {arXiv preprint arXiv:1508.06590},
  year   = {2016}
}

Comments

37 pages, 2 figures