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

  
@article{ECP3105,
	author = {Zhongyang Li},
	title = {Uniqueness of the infinite homogeneous cluster in the 1-2 model},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {},
	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.},
	pages = {no. 23, 1-8},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-3105},    
        url = {http://ecp.ejpecp.org/article/view/3105}}