Spin glass dynamics under a change in magnetic field

A barrier model is developed for spin glass dynamics. An ultrametric arrangement for spin glass states at magnetization M, with barrier heights increasing linearly with Hamming distance, is used to represent aging. Upon a change in magnetic field, with an associated change in Zeeman energy E(z), states with barrier heights Delta < E(z) rapidly transition to the new ground state magnetization. Calculation of the time rate of change of the magnetization for finite hierarchies yields results in agreement with experiment. Forms for the most probable values of the Parisi physical order parameter for infinite hierarchies, P(q), are extracted from experiment at representative temperatures.