Aging Relation for Ising Spin Glasses

We derive a rigorous dynamical relation on aging phenomena -- the aging relation -- for Ising spin glasses using the method of gauge transformation. The waiting-time dependence of the auto-correlation function in the zero-field-cooling process is equivalent with that in the field-quenching process. There is no aging on the Nishimori line; this reveals arguments for dynamical properties of the Griffiths phase and the mixed phase. The present method can be applied to other gauge-symmetric models such as the XY gauge glass.Comment: 9 pages, RevTeX, 2 postscript figure

Dynamical Gauge Theory for the XY Gauge Glass Model

Dynamical systems of the gauge glass are investigated by the method of the gauge transformation.Both stochastic and deterministic dynamics are treated. Several exact relations are derived among dynamical quantities such as equilibrium and nonequilibrium auto-correlation functions, relaxation functions of order parameter and internal energy. They provide physical properties in terms of dynamics in the SG phase, a possible mixed phase and the Griffiths phase, the multicritical dynamics and the aging phenomenon. We also have a plausible argument for the absence of re-entrant transition in two or higher dimensions.Comment: 3 figure

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 non-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