Monte Carlo evidence of non-equilibrium effects for ising model in a random field

Simulating an Ising model, up to sizes 150×150×150 in three and 225×225 in two dimensions, in a random field of strength ±H, we find a magnetization slowly decreasing with time if initially all spins are parallel. This decay is extremely slow for small random fields, so that a stable magnetization cannot be excluded. Below some "freezing" temperature, the system remains a single domain, with a finite magnetization in both two and three dimensions. If instead the system is cooled down in a constant random field, from temperatures above to temperatures below this freezing transition, then at the lower temperature the magnetization increases with time; this increase is very slow for large systems, with similar results in two and three dimensions.