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Gibbs State Uniqueness for Anharmonic Quantum Crystal with a Nonpolynomial Double-Well Potential | | Alexei L. Rebenko
; Valentin A. Zagrebnov
; | | Date: |
10 Jun 2004 | | Subject: | Mathematical Physics MSC-class: 60H30, 82B31 | math-ph math.MP | | Abstract: | We construct the Gibbs state for $
u$-dimensional quantum crystal with site displacements from $R^d$, $dgeq 1$, and with a one-site extit{non-polynomial} double-well potential, which has extit{harmonic} asymptotic growth at infinity. We prove the uniqueness of the corresponding {it Euclidean Gibbs measure} (EGM) in the extit{light-mass regime} for the crystal particles. The corresponding state is constructed via a cluster expansion technique for an arbitrary temperature $Tgeq 0$. We show that for all $Tgeq 0$ 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. | | Source: | arXiv, math-ph/0406018 | | Services: | Forum | Review | PDF | Favorites | |
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