Electronic Communications in Probability

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

Zhongyang Li

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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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Electron. Commun. Probab., Volume 19 (2014), paper no. 23, 8 pp.

Accepted: 23 April 2014
First available in Project Euclid: 7 June 2016

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Li, Zhongyang. Uniqueness of the infinite homogeneous cluster in the 1-2 model. Electron. Commun. Probab. 19 (2014), paper no. 23, 8 pp. doi:10.1214/ECP.v19-3105. https://projecteuclid.org/euclid.ecp/1465316725

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