Uniqueness of Infinite Homogeneous Clusters in 1-2 Model
  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. 
Zhongyang Li
math.PR math-ph math.MP