Dynamical systems of gauge-symmetric Ising spin glasses are investigated by the method of gauge transformation. Several exact relations are derived among dynamical quantities such as the equilibrium autocorrelation function and the nonequilibrium remanent magnetization. The same result as in the static case is obtained in terms of the equivalence of the ferromagnetic and the spin-glass order if the temperature and the randomness satisfy a special condition (Nishimori line). An exact equivalence of nonequilibrium relaxations in the spin-glass phase is derived between the remanent magnetization evolved from the strong-field limit and the autocorrelation function from a supercooled state. We also have a plausible argument for the absence of a re-entrant transition using the present dynamical relations.

75.10.Hk Classical spin models

75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects

75.10.Nr Spin-glass and other random models

82D30 Random media, disordered materials (including liquid crystals and spin glasses)

82C44 Dynamics of disordered systems (random Ising systems, etc.)

Condensed matter: electrical, magnetic and optical

Issue 13 ( 7 July 1995)