Moderate deviations for random field Curie-Weiss models

Abstract

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization $S_n$, which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number $m$, a positive real number $\lambda$, and a positive integer $k$ such that $(S_n-nm)/n^{\alpha }$ satisfies a moderate deviations principle with speed $n^{1-2k(1-\alpha )}$ and rate function $\lambda x^{2k}/(2k)!$, where $1-1/(2(2k-1))<\alpha <1$.

21 pages

References in corpus (2)

• Metastates in finite-type mean-field models: visibility, invisibility, and random restoration of symmetry
• The Curie-Weiss model with dynamical external field

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• Infinite volume Gibbs states and metastates of the random field mean-field spherical model
• On the accuracy of the normal approximation for the free energy in the REM
• A transfer principle for deviations principles