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LRO in Lattice Systems of Linear Classical and Quantum Oscillators. Strong Nearest-Neighbor Pair Quadratic Interaction

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Abstract

For systems of one-component interacting oscillators on the d-dimensional lattice, d>1, whose potential energy besides a large nearest-neighbour (n-n) ferromagnetic translation-invariant quadratic term contains small non-nearest-neighbour translation invariant term, an existence of a ferromagnetic long-range order for two valued lattice spins, equal to a sign of oscillator variables, is established for sufficiently large magnitude g of the n-n interaction with the help of the Peierls type contour bound. The Ruelle superstability bound is used for a derivation of the contour bound.

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  1. Institute of Mathematics, 3 Tereshchenkivska, Kyiv 4, Ukraine, 252601

    W. I. Skrypnik

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  1. W. I. Skrypnik
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Skrypnik, W.I. LRO in Lattice Systems of Linear Classical and Quantum Oscillators. Strong Nearest-Neighbor Pair Quadratic Interaction. Journal of Statistical Physics 100, 853–870 (2000). https://doi.org/10.1023/A:1018767109719

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