Mean field dilute ferromagnet I. High temperature and zero temperature behavior

Details Mean field dilute ferromagnet I. High temperature and zero temperature behavior Mean field dilute ferromagnet I. High temperature and zero temperature behavior

2008-01-31

arxiv.org/abs/0801.4940v4

Physics

Condensed Matter

Statistical Mechanics

38 pages

Scientific paper

10.1007/s10955-008-9575-2

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 the annealed model. Our results hold both for the Poisson and the Bernoulli versions of the model.

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