Bound states in the transfer matrix spectrum for general lattice ferromagnetic spin systems at high temperature

We obtain different properties of general d dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (beta much less than 1 ). Each model is characterized by a single site a priori spin distribution, taken to be even. We state our results in terms of the parameter alpha = < s(4)> - 3 < s(2)>(2) where < s(k)> denotes the kth moment of the a priori distribution. Associated with the model is a lattice quantum field theory that is known to contain particles. We show that for alpha > 0, beta small, there exists a bound state with mass below the two-particle threshold. For alpha < 0, bound states do not exist. The existence of the bound state has implications on the decay of correlations, i.e., the four-point function decays at a slower rate than twice that of the two-point function. These results are obtained using a lattice version of the Bethe-Salpeter equation in the ladder approximation. The existence and nonexistence results generalize to N-component models with rotationally invariant a priori spin distributions.