Uniqueness of the infinite homogeneous cluster in the 1-2 model

Zhongyang Li (University of Cambridge)


A 1-2 model configuration is a subset of edges of the hexagonal lattice such that each vertex is incident to one or two edges. We prove that for any translation-invariant Gibbs measure of 1-2 model, almost surely the infinite homogeneous cluster is unique.

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Pages: 1-8

Publication Date: April 23, 2014

DOI: 10.1214/ECP.v19-3105


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