Scaling and critical slowing down in random-field Ising systems

A simple scaling description of the ordering transition in random-field Ising systems is developed and supported by renormalization-group arguments in terms of a zero-temperature critical fixed point. The main prediction is that the characteristic relaxation time will diverge extremely rapidly as the critical point is approached: (^theta) with the correlation length and theta the ``violation of hyperscaling'' exponent (d-theta) =2-. Recent experiments which exhibit onset of hysteresis in a very narrow temperature range are discussed.