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Generalized canonical states. (English) Zbl 0589.60083

It is proved that the translation invariant canonical states satisfy a conditional variational principle. This is done in the setting of equilibrium statistical mechanics on a lattice with a slightly more general definition of canonical Gibbs states than the one introduced by H. O. Georgii [Z. Wahrscheinlichkeitstheor. Verw. Geb. 32, 277-300 (1975; Zbl 0296.60075)].
Subsequently, using variational techniques, we give an easy and natural proof of a result essentially obtained by R. L. Thompson [Mem. Am. Math. Soc. 150 (1974; Zbl 0327.60068)] and describing canonical states as Gibbs states associated to a linear combination of the potentials involved in the definition of the canonical states.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B05 Classical equilibrium statistical mechanics (general)
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References:

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