Abstract
In two recent papers Ruelle gave a heuristic theory of phase transitions, using some techniques introduced by Israel. He proves a version of Gibbs phase rule, assuming a differentiability condition for the pressure. Ruelle already pointed out that his condition cannot always hold. In this paper we prove that the interaction spaces which he considers are in general too large for his condition to hold. We also show that the version of the Gibbs phase rule which is a consequence of this condition does not hold in general. Moreover we give some constraints on the analyticity properties of the pressure.
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Communicated by E. Lieb
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Daniëls, H.A.M., van Enter, A.C.D. Differentiability properties of the pressure in lattice systems. Commun.Math. Phys. 71, 65–76 (1980). https://doi.org/10.1007/BF01230087
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DOI: https://doi.org/10.1007/BF01230087