Dynamical scaling and kinetic equations for heisenberg spin systems just below the critical temperature

Abstract

We propose an approximate set of kinetic equations to describe the time evolution of spin correlation functions below T c in a system with long-range interactions. In the ordered region, these equations lead to weakly damped spin waves, in exact agreement with the previous work of Vaks, Lakkin and Pikin. When T c is approached, spin waves persist for q ⪡ κ_, where κ_is the inverse correlation length but, for q ⪢ κ_, these kinetic equations continuously transform into the non-Markoffian equation previously derived by one of the authors and De Leener above F c . Moreover, dynamical scaling is microscopically justified in our model. Beyond the assumption of a large number of interacting neighbours, we also need the phenomenological hypothesis that, close to T c , the equilibrium properties appearing in our kinetic equations can be described by their correct (nonclassical) critical indices.