Long-time relaxation in disordered Ising chains

Abstract

We study the long-time relaxation of magnetization in a bond-disordered, one-dimensional kinetic Ising model. We show that with a ferromagnetic two-peaked distribution of the coupling constants, the magnetization at very long times varies as exp(-λ₀t-ct^1/3). For low enough temperatures, there is an intermediate time regime where the magnetization varies as exp(-λ₀t-bt^½). If the distribution of bond strengths varies as a power law near some maximum value J₀, we find that the magnetization at long times varies as exp(-λ₀t-ct^1/3(lnt)^⅔ ).