Seminario di fisica matematica
ore
17:00
presso Seminario I
Given an arbitrary finite dimensional Hamiltonian H_0,
we consider the model H=H_0+Delta H, where Delta H
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.