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Small mass implies uniqueness of Gibbs states of a quantum crystal. (English) Zbl 1149.82307
Summary: A model of interacting quantum particles performing one-dimensional anharmonic oscillations around their equilibrium positions which form a lattice \(\mathbb Z^d\) is considered. For this model, it is proved that the set of tempered Euclidean Gibbs measures is a singleton provided the particle mass is less than a certain bound \(m_*\), which is independent of the temperature \(\beta^{-1}\). This settles a problem that was open for a long time and is an essential improvement of a similar result, where the bound \(m_*\) depended on \(\beta\) in such a way that \(m_{\ast}(\beta)\rightarrow 0\) as \(\beta\rightarrow +\infty\).

MSC:
82B10 Quantum equilibrium statistical mechanics (general)
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