Non-exponential relaxation near a transition in the presence of disorder: The case of spin glasses

Abstract

Within the framework of a model which associates Kadanoff's renormalization with a hierarchical condition, we justify dynamic scaling (τ/τ ≈ (ξ/ξ₀)^z) and non-exponential relaxations (m(t) = t ^−1/zv at T = T _C). In the presence of some disorder the same model predicts β → α transition from a short-time regime where we observe activated T In t scaling for short-range effects, to a regime where we have stretched exponential behaviour and dynamic scaling (τ ≈ τ₀(1 – T _C/T)^−zv) for long-range effects.