Long-range order in Gibbs lattice classical linear oscillator systems - Skrypnik, W. I. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
The existence of the ferromagnetic long-range order (lro) is proved for Gibbs classical lattice systems of linear oscillators interacting via a strong polynomial pair nearest neighbor (n-n) ferromagnetic potential and other (nonpair) potentials that are weak if they are not ferromagnetic. A generalized Peierls argument and two different contour bounds are our main tools.