Dynamic properties of a spin-glass model at low temperatures

We present a semiphenomenological calculation of the low-temperature dynamic properties of a spin-glass model which is a two-dimensional Ising model with Gaussian random nearest-neighbor interactions. The distribution of the low-lying energy levels of the system is studied with the aid of a numerical program. The results of this investigation suggest a simple picture of independent spins and small-size clusters of spins flipping in a frozen-random-background field. This picure is similar to the phenomenological description of amorphous materials in terms of two-level systems. Distributions of the quantities which characterize a low-lying energy state in this picture are obtained numerically. A crude analytic calculation of these distributions is also included. These distributions are then used to calculate various low-temperature dynamic properties such as the time-dependent susceptibility, relaxation of the magnetization in an external magnetic field, and the remanent magnetization. We find that this simple description provides qualitative explanations of a large number of results obtained in previous Monte Carlo simulations.