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We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice quantum field model associated with d-dimensional lattice ferromagnetic classical N-component vector spin systems at high tem- perature (0 < fl ¿ 1). Each system is characterized by a single site "a priori" spin probability distribution. The energy-momentum spectrum exhibits isolated dispersion curves which are identified as single particles and multi-particle bands. Our two-particle bound state analysis is restricted to a ladder approximation of the Bethe-Salpeter equation, and the existence of bound states depend on whether or not Gaussian dom- ination for the four-point function is verified. It is known that two-particle bound states appear below the two-particle band if Gaussian domination does not hold. Here, we show that two two-particle bound states appear above the two-particle band if Gaussian domination is verified. We also show how the com- plete two-particle spectral pattern for these models can be understood by making a correspondence between the Bethe-Salpeter equation and a two-particle lattice Schrodinger Hamiltonian operator with attractive or repulsive spin-dependent delta potentials at the origin. A staggering transformation is used to relate the at- tractive and repulsive potential cases, as well as their associated Hamiltonians spectrum and eigenfunctions.

Transfer Matrix Spectrum for O(N) High Temperature Lattice Classical Ferromagnetic Spin Systems and Staggering Transformations