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Gibbs properties of the fuzzy Potts model on trees and in mean field

Olle Haeggstroem·Christof Kuelske
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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.

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Olle Haeggstroem, Christof Kuelske. 2003-10-31. Gibbs properties of the fuzzy Potts model on trees and in mean field. https://arxiv.org/abs/math/0310488

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