• DOI:10.1209/0295-5075/97/50008
• Corpus ID: 119563828

Mean-field models with short-range correlations

@article{Ostilli2011MeanfieldMW,
  title={Mean-field models with short-range correlations},
  author={Massimo Ostilli},
  journal={EPL (Europhysics Letters)},
  year={2011},
  volume={97},
  pages={50008}
}

• M. Ostilli
• Published 2 December 2011
• Mathematics
• EPL (Europhysics Letters)

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.