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