Mean-field models with short-range correlations

Abstract

Given an arbitrary finite dimensional Hamiltonian H_0, we consider the model H=H_0+ΔH, where ΔH is a generic fully connected interaction. By using the strong law of large numbers we easily prove that, for all such models, a generalized Curie-Weiss mean-field equation holds. Unlike traditional mean-field models the term H_0 gives rise to short-range correlations and, furthermore, when H_0 has negative couplings, first-order phase transitions and inverse transition phenomena may take place even when only two-body interactions are present. The dependence from a non uniform external field and finite size effects are also explicitly calculated. Partially, these results were derived long ago by using min-max principles but remained almost unknown.

7 pages, 1 figure

References in corpus (3)

• Crossover between a Short-range and a Long-range Ising model
• Effective field theory for models defined over small-world networks. First and second order phase transitions
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Cited by in corpus (3)

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