Abstract
We study theoretical and computational properties of the pressure function for subshifts of finite type on the integer lattice ℤd, multidimensional SOFT, which are called Potts models in mathematical physics. We give computable upper and lower bounds for the pressure, which can be arbitrary close to 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 entropy density as functions of two variables for the two-dimensional monomer-dimer model. The novelty of our approach is in avoiding the use of Gibbs measures.
Mathematics Subject Classification (2000). 05A16, 28D20, 37M25, 82B20, 82B26.
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Friedland, S., Peled, U.N. (2011). The Pressure, Densities and First-order Phase Transitions Associated with Multidimensional SOFT. In: Brändén, P., Passare, M., Putinar, M. (eds) Notions of Positivity and the Geometry of Polynomials. Trends in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0348-0142-3_11
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DOI: https://doi.org/10.1007/978-3-0348-0142-3_11
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