Mean-field models with short-range correlations
Department of Computational & Theoretical Sciences, IIUM - Kuantan, Pahang, Malaysia
2 Statistical Mechanics and Complexity Center (SMC), INFM-CNR SMC - Rome, Italy
Accepted: 30 January 2012
Given an arbitrary finite dimensional Hamiltonian H0, we consider the model H=H0+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 H0 gives rise to short-range correlations and, furthermore, when H0 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.
PACS: 02.70.Rr – General statistical methods / 02.50.Cw – Probability theory / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EPLA, 2012