A Heuristic theory of phase transitions

RESEAUX

SYSTEMES COMPLEXES

ESPACES DE BANACH

TRANSITIONS DE PHASE

Abstract : Let Z be a suitable Banach space of interactions for a lattice spin system. If n+1 thermodynamic phases coexist for ?0 ?Z, it is shown that a manifold of codimension n of coexistence of (at least) n+1 phases passes through ?0. There are also n+1 manifolds of codimension n?1 of coexistence of (at least) n phases; these have a common boundary along the manifold of coexistence of n+1 phases. And so on for coexistence of fewer phases. This theorem is proved under a technical condition (R) which says that the pressure is a differentiable function of the interaction at ?0 when restricted to some codimensionn affine subspace of Z. The condition (R) has not been checked in any specific instance, and it is possible that our theorem is useless or vacuous. We believe however that the method of proof is physically correct and constitutes at least a heuristic proof of the Gibbs phase rule.

RUELLE

P/76/149

IHES

10/1976

A4

25 f.

EN

TEXTE

PREPUBLICATION

P_76_149.pdf

1976

IHES

IHES

RUELLE

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_76_149/P_76_149.pdf

Oui

Bures-sur-Yvette

GIBBS

BANACH

ISRAEL

PIROGOV

SINAI

RUELLE

CHOQUET

HAHN

EUCLIDE

BOURBAKI

DYSON