Dynamical mean-field theory for spin glasses. I. Short-time properties in zero field

Abstract

The dynamical properties of a simple model of a spin glass are studied. The model has Gaussian random exchange interactions and Langevin dynamics. Following the ideas of Ma and Rudnick (1978) and of De Dominicis (1978), the spin glass phase is characterised by the presence of a finite limit of the spin autocorrelation function as t to infinity , i.e. by a delta-function part of it Fourier transform C( omega ). With a finite system in mind, this delta function is taken to have a small finite width. Then the fluctuation-dissipation theorem is imposed (before the infinite volume limit), forcing a corresponding low-frequency anomaly on the dynamical susceptibility. Solving self-consistently in mean-field theory for the order parameter, one then finds that the Almeida-Thouless instability of conventional theories is suppressed for all times shorter than the inverse width of the delta function in C( omega ). This theory is constructed for exactly zero external field; problems about the field dependence and possible relevance to experiment are discussed.