Representation and Poly-time Approximation for Pressure of Z2 Lattice Models in the Non-uniqueness Region
Representation theorem, Gibbs interactions, Widom–Rowlinson, Hard-core models
College of Natual Science and Mathematics, Mathematics
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 model, our results apply to every inverse temperature but the critical. For Widom–Rowlinson and hard-core models, 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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Adams, Stefan, et al. “Representation and Poly-Time Approximation for Pressure of Z2 Lattice Models in the Non-Uniqueness Region.” Journal of Statistical Physics, vol. 162, no. 4, 2016, p. 1031. doi: 10.1007/s10955-015-1433-4.