Excitations for lattice ferromagnetic classical spin systems at high temperature: noneven single-spin distributions

Abstract

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (beta<<1). Each model is characterized by a single-site a priori spin probability distribution taken to be noneven. We state our results in terms of the parameter alpha=(<&smacr; (4)>-3<&smacr; (2)>(2)-<&smacr; (3)>(2)<&smacr; (2)>(-1))/(<&smacr; (4)>-<&smacr; (2)>(2)-<&smacr; (3)>(2)<&smacr; (2)>(-1)), where &smacr;=s-<s>, and <s(k)> denotes the kth moment of the single-site distribution. Associated with the model is a lattice quantum field theory which is known to contain a particle of mass m approximately ln beta. Assuming <&smacr;(3)> not equal0 we show that for alpha>0, beta small, there exists a bound state with mass below the two-particle threshold 2m. For alpha<0 bound states do not exist. These results are obtained using a Bethe-Salpeter (BS) equation in the ladder approximation in conjunction with a representation for the inverse of the two-point function designed to analyze the spectrum below but close to 2m.