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 ξ j . 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 ξ j , 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.
KeywordsPhase Transition Ising Model Cluster Expansion Droplet Model Dimensional Ising Model
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- [Domb and Green, 1972-], [Ruelle, 1969], [Stanley, 1971].Google Scholar