Uniqueness of the Infinite Cluster for Stationary Gibbs States
Open Access
- 1 October 1989
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 17 (4) , 1403-1415
- https://doi.org/10.1214/aop/1176991161
Abstract
We prove, in all dimensions, that for a stationary Gibbs state with finite range or rapidly decreasing interaction, there is at most one infinite percolation cluster. This implies that the connectivity function is bounded away from 0.Keywords
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