GIBBSIANNESS AND NON-GIBBSIANNESS IN DIVIDE AND COLOR MODELS

• 成果类型: Article
• 署名作者: Balint, Andras
• 署名单位: Vrije Universiteit Amsterdam
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP518
• 发表日期: 2010
• 页码: 1609-1638
• 关键词: fuzzy potts-model; percolation models; transformations; probability; clusters

摘要

For parameters p is an element of [0, 1] and q > 0 such that the Fortum Kasteleyn (FK) random-cluster measure Phi(Zd)(p,q) for Z(d) with parameters p and q is unique. the q-divide and color [DaC(q)] model on Z(d) is defined as follows First, we draw a bond confitmration with distribution Phi(Zd)(p,q) Then, to each (FK) cluster (i e. to every vertex in the FK cluster). independently for different FK clusters. we assign a spin value from the set {1, 2...s} in such a way that spin t has probability a(t) In this paper. we prove that the iesulting measure on spin configurations is a Gibbs measure for small values of p and is not a Gibbs measure for large p. except in the special case of q is an element of {2, 3...}, a(1) = a(2) = = a(s) = 1/q, when the DaC(q) model coincides with the q-state Potts model