Size-dependence of relaxation in random-field Ising model

Monte Carlo simulations were made of two- and three-dimensional Ising models containing up to 150³ and 1395² sites in a randomly oriented field ±H. A spontaneous magnetization was observed to build up at low enough temperatures, even if initially the spins were disordered. The time required for this build-up was observed to increase with some power of the system size for short times, and possibly exponentially with the square root of the length for larger times.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday