Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (β≪1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m≅−lnβ in the energy-momentum spectrum. If α≡〈s4〉−3〈s2〉2 0 we show that the only mass spectrum in (m, 2m) is a bound state of mass mb=2m+ln(1−γ)+O(β), where γ=α(α+2〈s2〉2)−1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.