Long-range order in quantum lattice systems of linear oscillators

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