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.

Mean field dilute ferromagnet: high temperature and zero temperature behavior / LUCA DE, Sanctis; Guerra, Francesco. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 132:(2008), pp. 759-785. [10.1007/s10955-008-9575-2]

Mean field dilute ferromagnet: high temperature and zero temperature behavior

GUERRA, Francesco
2008

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.
2008
01 Pubblicazione su rivista::01a Articolo in rivista
Mean field dilute ferromagnet: high temperature and zero temperature behavior / LUCA DE, Sanctis; Guerra, Francesco. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 132:(2008), pp. 759-785. [10.1007/s10955-008-9575-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/5699
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