Authors: Luca De Sanctis Francesco Guerra
Publish Date: 2008/06/10
Volume: 132, Issue: 5, Pages: 759-
Abstract
We study the mean field dilute model of a ferromagnet We find and prove an expression for the free energy density at high temperature and at temperature zero We find the critical line of the model separating the phase with zero magnetization from the phase with symmetry breaking We also compute exactly the entropy at temperature zero which is strictly positive The physical behavior at temperature zero is very interesting and related to infinite dimensional percolation and suggests possible behaviors at generic low temperatures Lastly we provide a complete solution for a partially annealed model Our results hold both for the Poisson and the Bernoulli versions of the model
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