Metastability and Depinning Threshold in the Random Field Ising Model

Abstract

AbstractA unified description of the depinning threshold Ec for domain walls in the random field Ising model is given. The coherence length Rc ∼ E of the metastable state is proportional to h−vh, where h is the random field amplitude. For broad walls, the results interpolate between recent findings of Bruinsma and Aeppli (vH = 4/(5 – d)) valid at temperatures T ≪ Th(t) and those of Villain (vH = 2) for Th(t) < T ≪ Tco. Tco is the transition temperature of the pure system and Th(t) ∼ h2(3 – d)/(5 – d)/In t, t denotes the time. For narrow walls vH = 2/(3 – d) is found for T < Th(t), vH = 2 for T > Th(t), Th(t) ∼ h2(2 – d)/(3 – d)/In t and d ≦ 3. For d → 3 an exponential dependence is expected of Rc on h−2. Vacancies are found to be decisive for wall pinning in diluted antiferromagnets in small external fields.