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Statistical mechanics of a one-dimensional lattice gas


We study the statistical mechanics of an infinite one-dimensional classical lattice gas. Extending a result ofvan Hove we show that, for a large class of interactions, such a system has no phase transition. The equilibrium state of the system is represented by a measure which is invariant under the effect of lattice translations. The dynamical system defined by this invariant measure is shown to be aK-system.

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Ruelle, D. Statistical mechanics of a one-dimensional lattice gas. Commun.Math. Phys. 9, 267–278 (1968). https://doi.org/10.1007/BF01654281

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