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

Abstract

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 temperature (0 < β 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 domination 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 complete two-particle spectral pattern for these models can be understood by making a correspondence between the Bethe-Salpeter equation and a two-particle lattice Schrödinger Hamiltonian operator with attractive or repulsive spin-dependent delta potentials at the origin. A staggering transformation is used to relate the attractive and repulsive potential cases, as well as their associated Hamiltonians spectrum and eigenfunctions.

"Espectro de excitação para modelos quânticos na rede"

“…A aplicabilidade do modelo de spins O(N ) a uma variedade tão grande de modelos nas proximidades de um ponto crítico é a manifestação da universalidade em fenômenos críticos (ver [7,8] [9,10,11,12] foram obtidas propriedades análogas as demonstradas aqui. O trabalho feito aqui, está sintetizado na referência [13].…”

“…Para um momento total fixo p, a banda é determinada pela equação w( p 1 ) + w( p 2 ), com a restrição 13) sendo π = (π, ..., π), ela começa no "limiar de duas partículas" 2m e termina em 2m+W .…”