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 τ will diverge extremely rapidly as the critical point is approached: τ∼exp(${\xi }^{\mathrm{theta}}$) with ξ the correlation length and theta the ‘‘violation of hyperscaling’’ exponent (d-theta)ν=2-α. Recent experiments which exhibit onset of hysteresis in a very narrow temperature range are discussed.