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Transactions of the American Mathematical Society

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Nonstandard analysis and lattice statistical mechanics: a variational principle


Author: A. E. Hurd
Journal: Trans. Amer. Math. Soc. 263 (1981), 89-110
MSC: Primary 82A68; Secondary 03H10, 28A20, 60K35
DOI: https://doi.org/10.1090/S0002-9947-1981-0590413-2
MathSciNet review: 590413
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0590413-2
Keywords: Lattice statistical mechanics, generalized equilibrium (Gibbs) state, variational principle, limiting configuration space
Article copyright: © Copyright 1981 American Mathematical Society

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