Pressure and equilibrium measures for actions of amenable groups on the space of configurations

The model of statistical physics on a countable amenable group $G$ is considered. For the natural action of $G$ on the space of configurations $S^G$, $|S|<\infty$, and for any closed invariant set $X\subset S^G$ we prove that there exists pressure which corresponds to a potential with finite norm on $X$ (in the sense of the limit with respect to any Følner sequence of sets in $G$). The existence of an equilibrium measure is established.
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