Large deviations principle for random field Curie-Weiss models

Details Large deviations principle for random field Curie-Weiss models Large deviations principle for random field Curie-Weiss models

2011-12-22

arxiv.org/abs/1112.5380v1

Mathematics

Probability

11 pages

Scientific paper

The random field Curie-Weiss model is derived from the Curie-Weiss model by replacing the constant and deterministic external magnetic field by a local random external field which interacts with each spin of the system. In this setting, we calculate the quenched free energy and the annealed free energy. We prove a Large Deviations Principle for the so called {\it magnetization per spin} $S_n/n$ with respect to the associated Gibbs measure, where $S_n/n$ is the scaled partial sum of spins. We also show how our result is applied and discuss the behaviour of the rate function for different choices of the distribution of the random external magnetic field.

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