Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field

O. Haggstrom, C. Kuelske

2004, v.10, №3, 477-506

ABSTRACT

We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that non-Gibbsianness of the fuzzy Potts model happens exactly for those temperatures where the underlying Potts model has multiple Gibbs measures.

Keywords: Potts model,fuzzy Potts model,Gibbs measures,non-Gibbsian measures,trees,mean-field models

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