Absence of Critical Points for a Class of Quantum Hierarchical Models |
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Authors: | S. Albeverio Y. G. Kondratiev Y. V. Kozitsky |
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Affiliation: | Fakult?t für Mathematik, Ruhr-Universit?t Bochum, Bochum, Germany, DE BiBoS Research Centre Bielefeld, Bielefeld, Germany, DE Lviv Academy of Commerce, Lviv, Russia, RU
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Abstract: | Hierarchical models of quantum anharmonic oscillators with a polynomial anharmonicity and interaction decaying as (distance)-1-λ are considered. For a class of such models (including ϕ4-type anharmonicity ones), it is shown that the critical fluctuations of the position operator are absent, for all λ > 0 and all temperatures, provided the oscillators mass in less than some threshold value depending on the anharmonicity parameters. This result may be interpreted as a rigorous mathematical justification of physical arguments showing that quantum fluctuations can damp phase transitions. Received: 12 April 1996 / Accepted: 25 October 1996 |
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