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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2006

Gibbs State Uniqueness for Anharmonic Quantum Crystal with a Nonpolynomial Double-Well Potential

Résumé

We construct the Gibbs state for $\nu$-dimensional quantum crystal with site displacements from $\R^d$, $d\geq 1$, and with a one-site \textit{non-polynomial} double-well potential, which has \textit{harmonic} asymptotic growth at infinity. We prove the uniqueness of the corresponding {\it Euclidean Gibbs measure} (EGM) in the \textit{light-mass regime} for the crystal particles. The corresponding state is constructed via a cluster expansion technique for an arbitrary temperature $T\geq 0$. We show that for all $T\geq 0$ the Gibbs state (correlation functions) is analytic with respect to external field conjugated to displacements provided that the mass of particles $m$ is less than a certain value $m_* >0$. The high temperature regime is also discussed.

Dates et versions

hal-00122397 , version 1 (31-12-2006)

Identifiants

Citer

Alexei L. Rebenko, Valentin A. Zagrebnov. Gibbs State Uniqueness for Anharmonic Quantum Crystal with a Nonpolynomial Double-Well Potential. Journal of Statistical Mechanics: Theory and Experiment, 2006, pp.P09002. ⟨10.1088/1742-5468/2006/09/P09002⟩. ⟨hal-00122397⟩
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