Metastable states, internal field distributions and magnetic excitations in spin glasses

Abstract

The properties of the metastable states in vector spin glasses are studied in the context of the long-range model of Sherrington and Kirkpatrick (1975), generalised to m-component spins. The total number of metastable states is calculated exactly, as is their distribution over energy for a range of energies. For the planar (m=2) and Heisenberg (m=3) models, the dispersion in energy of these states is found to be small. The distribution P(H) of internal fields is calculated as a function of the energy of the metastable state and the existence of a 'hole' at small fields established for m>or=2. For m=2 the calculated P(H) is in good agreement with the data of Palmer and Pond (1979). The dynamics of the model are studied for m=3 using the semiclassical equations of motion for small deviations from equilibrium. The density of states of the normal modes and the local dynamical susceptibility are calculated exactly. Generalisations to finite temperature are discussed in terms of the solutions of the Thouless-Anderson-Palmer equations for m-component spins.