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arXiv · 1508.06590

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

Stefan Adams·Raimundo Briceño·Brian Marcus·Ronnie Pavlov
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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.

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Stefan Adams, Raimundo Briceño, Brian Marcus, Ronnie Pavlov. 2015-08-26. Representation and poly-time approximation for pressure of $\mathbb{Z}^2$ lattice models in the non-uniqueness region. https://doi.org/10.1007/s10955-015-1433-4

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