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Long-range order in quantum lattice systems of linear oscillators

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Abstract

The existence of the ferromagnetic long-range order is proved for equilibrium quantum lattice systems of linear oscillators whose potential energy contains a strong ferromagnetic nearest-neighbor (nn) pair interaction term and a weak nonferromagnetic term under a special condition on a superstability bound. It is shown that the long-range order is possible if the mass of a quantum oscillator and the strength of the ferromagnetic nn interaction exceed special values. A generalized Peierls argument and a contour bound, proved with the help of a new superstability bound for correlation functions, are our main tools.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    W. I. Skrypnik

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  1. W. I. Skrypnik
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1407–1424, October, 2006.

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Skrypnik, W.I. Long-range order in quantum lattice systems of linear oscillators. Ukr Math J 58, 1597–1615 (2006). https://doi.org/10.1007/s11253-006-0156-8

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  • DOI: https://doi.org/10.1007/s11253-006-0156-8

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