We consider Bernoulli percolation on a locally finite quasi-transitive unimodular graph and prove that two infinite clusters cannot have infinitely many pairs of vertices at distance 1 from one another or, in other words, that such graphs exhibit “cluster repulsion.” This partially answers a question of Häggström, Peres and Schonmann.
"Neighboring clusters in Bernoulli percolation." Ann. Probab. 34 (6) 2332 - 2343, November 2006. https://doi.org/10.1214/009117906000000485