Meanfield models with shortrange 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 CurieWeiss meanfield equation holds. Unlike traditional meanfield models, the term H_{0} gives rise to shortrange correlations and, furthermore, when H_{0} has negative couplings, firstorder phase transitions and inverse transition phenomena may take place even when only twobody interactions are present. The dependence from a nonuniform external field and finitesize effects are also explicitly calculated. Partially, these results were derived long ago by using minmax principles but remained almost unknown.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 March 2012
 DOI:
 10.1209/02955075/97/50008
 arXiv:
 arXiv:1112.0395
 Bibcode:
 2012EL.....9750008O
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Mathematics  Probability;
 60F15;
 82Bxx
 EPrint:
 7 pages, 1 figure