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A strong variational principle for continuous spin systems

Published online by Cambridge University Press:  14 July 2016

Marc Pirlot
Marc Pirlot*
Affiliation:
Université de l'Etat à Mons
*
∗Postal address: Université de l'Etat à Mons, Place Warocqué 17, 7000 Mons, Belgium.
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Abstract

We prove in the setting of the system of unbounded spins developed by Lebowitz and Presutti, a strong variational principle analogous to Lanford and Ruelle's for discrete spins. We establish this result for finite-range regular and superstable potentials satisfying a condition which enables us to define the thermodynamic energy of the system.

Keywords

EQUILIBRIUM STATISTICAL MECHANICSCONTINUOUS SPINS SYSTEMSVARIATIONAL PRINCIPLE
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 47 - 58
Copyright
Copyright © Applied Probability Trust 1980 

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References

Föllmer, H. (1973) On entropy and information gain in random fields. Z. Wahrscheinlichkeitsth. 26, 207–217.Google Scholar
Lanford, O. E. and Ruelle, D. (1969) Observables at infinity and states with short range correlations in statistical mechanics. Commun. Math. Phys. 13, 194–215.CrossRefGoogle Scholar
Lebowitz, J. L. and Presutti, E. (1976) Statistical mechanics of systems of unbounded spins. Commun. Math. Phys. 50, 195–218.Google Scholar
Preston, C. (1976) Random Fields. Lecture Notes in Mathematics 534, Springer-Verlag, Berlin.Google Scholar
Royer, G. (1977) Etude des champs euclidiens sur un réseau Z v . J. Math. Pures Appl. 56, 455–478.Google Scholar
Ruelle, D. (1967) A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule. Commun. Math. Phys. 5, 324–329.CrossRefGoogle Scholar
Ruelle, D. (1969) Statistical Mechanics: Rigorous Results. Benjamin, New York.Google Scholar
Ruelle, D. (1976) Probability estimates for continuous spin systems. Commun. Math. Phys. 50, 189–194.Google Scholar