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arXiv · 1112.0395

Mean-field models with short-range correlations

M. Ostilli
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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.

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BibTeXRIS

M. Ostilli. 2012-03-16. Mean-field models with short-range correlations. https://doi.org/10.1209/0295-5075%2F97%2F50008

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