ANALYTICAL APPROXIMATIONS FOR THE HIERARCHICALLY CONSTRAINED KINETIC ISING CHAIN

The hierarchically constrained kinetic Ising model in one dimension is reviewed, and the results of several analytical approaches to the mod el are presented. Two standard approximation schemes, an effective-med ium approximation and a mode-coupling approximation, are shown to fail . A new class of approximations, termed cluster approximations, is bet ter suited for the model. It yields good results for the spin autocorr elation function, and also elucidates important general properties of the model-its connection with defect-diffusion models and the asymptot ic long-time behavior of the autocorrelation function.