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Zbl 0743.60030
Wu, L.M.
Grandes déviations pour les mesures de Gibbs lorsque la température tend vers zéro. (Large deviations for Gibbs measures when the temperature tends to zero.). (French)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 27, No.3, 273-289 (1991). ISSN 0246-0203

Summary: We give a quantitative description of phase transition phenomena at low temperature. More precisely, for a statistical mechanic system on the lattice $\bbfZ\sp d$ given by interaction potential, let $\mu\sp \beta\sb \eta$ be the Gibbs measure corresponding to the inverse temperature $\beta$ and the ground state $\eta$. When $\beta$ increases to $+\infty$, we obtain an estimation of large deviation of $\mu\sp \beta\sb \eta$: the lower bound for general cases and the upper bound only for the Ising ferromagnet. In both cases, the rate function is given by the relative Hamiltonian $H(.\mid \eta)$.

MSC 2000:: *60F10 Large deviations

Keywords: phase transition phenomena; interaction potential; Gibbs measure; Ising ferromagnet

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