Magnetizations are introduced to the Generalized Random Energy Model (GREM) and numerical simulations on ac susceptibility is made for direct comparison with experiments in glassy materials. Prominent dynamical natures of spin glasses, i.e., memory effect and reinitialization, are reproduced well in the GREM. The existence of many layers causing continuous transitions is very important for the two natures. Results of experiments in other glassy materials such as polymers, supercooled glycerol and orientational glasses, which are contrast to those in spin glasses, are interpreted well by the Single-layer Random Energy Model.
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