ISSN:
1572-9613
Keywords:
Large deviations
;
Kac potentials
;
spin vector models
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We consider the one-dimensional planar rotator and classical Heisenberg models with a ferromagnetic Kac potential J γ(r)=γJ(yr), J with compact support. Below the Lebowitz-Penrose critical temperature the limit (mean-field) theory exhibits a phase transition with a continuum of equilibrium states, indexed by the magnetization vectors m β s, s any unit vector and m β the Curie–Weiss spontaneous magnetization. We prove a large-deviation principle for the associated Gibbs measures. Then we study the system in the limit γ ↓ 0 below the above critical temperature. We prove that the norm of the empirical spin average in blocks of order γ−1 converges to m β, uniformly in intervals of order γ−p , for any p ≥ 1. We also give a lower bound to the scale on which the change of phase occurs, by showing that the empirical spin average is approximately constant on intervals having length of order γ-1-λwith λ∈(0,1) small enough.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1023095619236
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