Damage spreading in random field systems

We investigate how a quenched random field influences the damage-spreading transition in kinetic Ising models. To this end we generalize a recent master equation approach and derive an effective field theory for damage spreading in random-field systems. This theory is applied to the Glauber Ising model with a bimodal random-field distribution. We find that the random field influences the spreading transition by two different mechanisms with opposite effects. First, the random field favours the same particular direction of the spin variable at each site in both systems which reduces the damage. Second, the random field suppresses the magnetization which in turn tends to increase the damage. The competition between these two effects leads to a rich behaviour.