WIAS Preprint No. 878, (2003)

Gibbs properties of the fuzzy potts model on trees and in mean fields



Authors

  • Häggström, Olle
  • Külske, Christof

2010 Mathematics Subject Classification

  • 82B20 82B26

2008 Physics and Astronomy Classification Scheme

  • 05.50.+q 02.50.Cw

Keywords

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

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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