Uniqueness of Infinite Homogeneous Clusters in 1-2 Model
Probability
2012-10-15 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1210.3525,
title = {Uniqueness of Infinite Homogeneous Clusters in 1-2 Model},
author = {Zhongyang Li},
journal= {arXiv preprint arXiv:1210.3525},
year = {2012}
}