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We prove that critical percolation on any quasi-transitive graph ofexponential volume growth does not have a unique infinite cluster. This allowsus to deduce from earlier results that critical percolation on any graph inthis class does not have any infinite clusters. The result is new when thegraph in question is either amenable or nonunimodular.

Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters