Glauber dynamics of the SK model: theory and simulations in the low-temperature phase

Abstract

The low-temperature Glauber dynamics of the Sherrington-Kirkpatrick spin-glass model is studied using a combination of theory and computer simulations. The theoretical approach follows the spirit of Mori's continuous fraction expansion. The predicted amplitude of the long-time decay of the time-dependent equilibrium spin-spin correlation function agrees well with the Glauber dynamics simulation results. The theory predicts a universal dynamic exponent of in the low-temperature phase. The simulations cannot distinguish between a universal exponent and a temperature-dependent one.