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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≡〈s 4〉−3〈s 2〉20 we show that the only mass spectrum in (m, 2m) is a bound state of mass m b=2m+ln(1−γ)+O(β), where γ=α(α+2〈s 2〉2)−1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results. |
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