Representation and poly-time approximation for pressure of mathbb{Z}² lattice models in the non-uniqueness region
classification
🧮 math.DS
math-phmath.MPmath.PR
keywords
applypressurehard-coremodelspottsrepresentationwidom-rowlinsonalgorithms
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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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