The existence of an unbounded order parameter (magnetization) is established for a broad class of lattice Gibbs (equilibrium) systems of linear oscillators interacting via a strong pair nearest-neighbor polynomial potential and other many-body potentials. The considered systems are characterized by a general polynomial short-range interaction potential energy that generates Gibbs averages satisfying two generalized GKS inequalities.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 4, pp. 538–547, April, 2009.
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Skrypnik, W.I. On an unbounded order parameter in lattice equilibrium GKS-type oscillator systems. Ukr Math J 61, 645–656 (2009). https://doi.org/10.1007/s11253-009-0230-0
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DOI: https://doi.org/10.1007/s11253-009-0230-0