Phase Transitions and Critical Points

Abstract

For statistical behavior in a family ξ _i of random variables, we required in Chapter 2 the property of almost independence: ξ _i should be almost independent of all but a finite number of ξj This property, in the sense of short range stable forces, was satisfied by the examples of Chapter 2. We now draw a further distinction of weak vs. strong interactions. Weak means that ξ _i should be almost independent of all ξj j ≠ i, while strong means that ξ _i is strongly correlated to a finite number of ξ _j , j ≠ i. The weak coupling situations are handled by expansions, as in Chapter 2, and should be regarded as perturbations of an infinite tensor product, zero interaction model.