One-dimensional time-dependent Ising model in ramdom magnetic fields

The relaxation to equilibrium of a spin chain in a random magnetic field H is investigated; periodic, patchwise and purely random distributions are studied. To close the set of kinetic equations, the Bragg-Williams approximation (BWA) and a triplet closure approximation (TCA) are applied, and stationary solutions show agreement with those obtained from equilibrium statistical mechanics. However, BWA and TCA time-dependent solutions exhibit differences which are not only quantitative but qualitative for certain values of the coupling constant J. The TCA is applied to analyze the relaxation far from equilibrium and the relaxation function of magnetization departs from a single exponential and significant differences exist between both cases J > 0 and J < 0. For the antiferromagnetic coupling constant, the relaxation function of the magnetization first decays quickly, then becomes negative, passes through a minimum and tends to equilibrium slowly. On the other hand, differences are significant for various distributions of H, especially in the antiferromagnetic case.