Relaxation of magnetisation in one-dimensional random Glauber model

Abstract

Numerical calculations for the relaxation of magnetisation in a one-dimensional random Glauber model are described for two probability distributions of the exchange constant. One probability distribution allows both the ferromagnetic and antiferromagnetic interactions, while the other only ferromagnetic. The Glauber kinetic equations for chains of 5000 and 9000 spins are solved for the appropriate initial conditions by the method of Laplace transformation followed by a continued-fraction expansion of the required Green function. For the probability distribution with both ferromagnetic and antiferromagnetic interactions, it is found that the magnetisation decay is characterised by two time regimes, a fast exponential-like decay followed by a slow decay, in which the magnetisation decays logarithmically with time. The slow decay regime is interpreted in terms of thermally activated tunnelling through energy barriers. A distribution function for the energy barriers is explicitly obtained.