Nonequilibrium relaxation study of Ising spin glass models

As an analysis of equilibrium phase transitions, the nonequilibrium relaxation method is extended to the spin glass (SG) transition. The +/-J Ising SG model is analyzed for three-dimensional (cubic) lattices up to the linear size of L=127 and for four-dimensional (hypercubic) lattice up to L=41. These sizes of systems are quite large as compared with those calculated, so far, by equilibrium simulations. As a dynamical order parameter, we calculate the clone correlation function (CCF) Q(t,t(w))equivalent to[<S-i((1)) (t+t(w))S-i((2)) (t+t(w))>F], which is a spin correlation of two replicas produced after the waiting time t, from a simple starting state. It is found that the CCF shows an exponential decay in the paramagnetic phase, and a power-law decay after aginglike development (t much greater thant(w)) in the SG phase. This provides a reliable upper bound of the transition temperature T-g. It is also found that a scaling relation Q(t,tw) = t(w)(-lambda) (q)(Q) over bar (t/t(w)), holds just around the transition point providing the lower bound of T-g. Together with these two bounds, we propose a new dynamical way for the estimation of T-g from much larger systems. In the SG phase, the power-law behavior of the CCF for t much greater thant(w) suggests that the SG phase in short-range Ising models has a rugged phase space.