Nonstandard analysis and lattice statistical mechanics: a variational principle

Hurd, A. E.

doi:10.1090/S0002-9947-1981-0590413-2

Nonstandard analysis and lattice statistical mechanics: a variational principle
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by A. E. Hurd PDF

Trans. Amer. Math. Soc. 263 (1981), 89-110 Request permission

Abstract:

Using nonstandard methods we construct a configuration space appropriate for the statistical mechanics of lattice systems with infinitely many particles and infinite volumes. Nonstandard representations of generalized equilibrium measures are obtained, yielding as a consequence a simple proof of the existence of standard equilibrium measures. As another application we establish an extension for generalized equilibrium measures of the basic variational principle of Landord and Ruelle. The same methods are applicable to continuous systems, and will be presented in a later paper.

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