Abstract
The authors study the statics and long-time dynamics of a spin glass on a family of hierarchical lattices. The statics may be solved exactly on these lattices, and they treat the dynamics in a physically motivated low-temperature approximation, retaining only the slowest mode at each renormalization step. The results are generally in good agreement with Monte Carlo simulations in two and three dimensions. In particular, they find dynamical scaling at the spin glass transition in three dimensions, with a dynamical exponent z=6.5. The spin autocorrelation function at Tg decays like t-x with x=0.05. A new result for statics which is used in the dynamics calculation is that for the magnetic exponent ych at the critical point, which is found to be 2.65. Above Tg, the autocorrelation function can be fitted in a wide intermediate time range by a Kohlrausch form, but in this model this is only a consequence of a crossover in the renormalization flow and has no fundamental dynamical significance.
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