Abstract
First it is shown that each extremal equilibrium state is representable as limit of Gibbs states in finite volumes, and that an analogous statement holds for extremal invariant equilibrium states. Secondly we prove that for negative pair interactions only one equilibrium state exists which minimizes (resp. maximizes) the particle density, but that in general there are more than two extremal invariant equilibrium states with the same particle density. In this context, periodic interactions are studied.
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Georgii, HO. Two remarks on extremal equilibrium states. Commun.Math. Phys. 32, 107–118 (1973). https://doi.org/10.1007/BF01645650
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DOI: https://doi.org/10.1007/BF01645650