Approach to the ground state in disordered magnetic systems: Simulated annealing study

We present results of detailed simulated annealing studies on several models of bond-disordered Ising ferromagnets in two dimensions, both with distribution of couplings extending down to zero and with a cutoff greater than zero in the distribution. We find that in each of these cases the residual energy after cooling, ΔE(r), can be represented as a power law of the cooling rate r, i.e., ΔE(r)=${\mathrm{Ar}}^x$. Results for the cooling-rate dependence of the magnetization, M(r), are also discussed.