Issue |
EPL
Volume 97, Number 5, March 2012
|
|
---|---|---|
Article Number | 50008 | |
Number of page(s) | 6 | |
Section | General | |
DOI | https://doi.org/10.1209/0295-5075/97/50008 | |
Published online | 05 March 2012 |
Mean-field models with short-range correlations
1
Department of Computational & Theoretical Sciences, IIUM - Kuantan, Pahang, Malaysia
2
Statistical Mechanics and Complexity Center (SMC), INFM-CNR SMC - Rome, Italy
a
massimo.ostilli@roma1.infn.it
Received:
1
December
2011
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
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