Statics and Dynamics of a Two-Dimensional Ising Spin-Glass Model

Abstract

The temperature and field dependence of spatial correlations and relaxation times are investigated in detail by Monte Carlo simulations for a two-dimensional Ising spin-glass model. There is no transition, but, in zero field, barrier heights and correlation range increase smoothly at low temperatures. This increase does not seem to be fast enough to explain experiments. In a field, barrier heights and the correlation length tend to a finite limit as $T\to 0$. Points in the $h-T$ plane with constant relaxation time satisfy $T\left(h\right)-T\left(0\right)\mathrm{}\propto h^{\frac{2}{3}}$ at moderately low temperatures.