EXACT DYNAMICAL RELATIONS OF ISING SPIN-GLASSES

We investigate dynamical systems of gauge symmetric Ising spin glasses using the method of the gauge transformation. Several exact relations are derived among dynamical quantities such as the equilibrium auto-correlation function and the nan-equilibrium 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 non-equilibrium relaxations in the spin glass phase is derived between the remanent magnetization evolved from the strong field limit and the auto-correlation function from a supercooled state. We also have a plausible argument for the absence of re-entrant transition.