Abstract
Let \((\Sigma^{+}_{G}, \sigma)\) be a one-sided transitive subshift of finite type, where symbols are given by a finite spin set S, and admissible transitions are represented by an irreducible directed graph G⊂S×S. Let \(H : \Sigma^{+}_{G}\to\mathbb{R}\) be a locally constant function (that corresponds with a local observable which makes finite-range interactions). Given β>0, let μ βH be the Gibbs-equilibrium probability measure associated with the observable −βH. It is known, by using abstract considerations, that {μ βH } β>0 converges as β→+∞ to a H-minimizing probability measure \(\mu_{\min}^{H}\) called zero-temperature Gibbs measure. For weighted graphs with a small number of vertices, we describe here an algorithm (similar to the Puiseux algorithm) that gives the explicit form of \(\mu_{\min}^{H}\) on the set of ground-state configurations.
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E. Garibaldi supported by CNPq posdoc scholarship.
P. Thieullen supported by ANR BLANC07-3_187245, Hamilton-Jacobi and Weak KAM Theory.
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Garibaldi, E., Thieullen, P. Description of Some Ground States by Puiseux Techniques. J Stat Phys 146, 125–180 (2012). https://doi.org/10.1007/s10955-011-0357-x
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DOI: https://doi.org/10.1007/s10955-011-0357-x