The pressure, densities and first order phase transitions associated with multidimensional SOFT

Details The pressure, densities and first order phase transitions associated with multidimensional SOFT The pressure, densities and first order phase transitions associated with multidimensional SOFT

2009-06-28

arxiv.org/abs/0906.5176v4

Physics

Mathematical Physics

33 pages, 2 figures

Scientific paper

We study theoretical and computational properties of the pressure function for subshifts of finite type on the integer lattice $\Z^d$, multidimensional SOFT, which are called Potts models in mathematical physics. We show that the pressure is Lipschitz and convex. We use the properties of convex functions to show rigorously that the phase transition of the first order correspond exactly to the points where the pressure is not differentiable. We give computable upper and lower bounds for the pressure, which can be arbitrary close the values of the pressure given a sufficient computational power. We apply our numerical methods to confirm Baxter's heuristic computations for two dimensional monomer-dimer model, and to compute the pressure and the density entropy as functions of two variables for the two dimensional monomer-dimer model.

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