Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field
2004, v.10, Issue 3, 477-506
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