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.
English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 10, pp 1597-1615.
Citation Example: Skrypnik W. I. Long-range order in quantum lattice systems of linear oscillators // Ukr. Mat. Zh. - 2006. - 58, № 10. - pp. 1407–1424.