Domain growth and thermal relaxation in spin glasses

The low-temperature growth of correlated domains in nearest neighbor Gaussian Ising spin glases in 2, 3 and 4 dimensions is studied by two different Monte Carlo techniques. The first is patterned on the ‘lid’ method previously proposed by the authors. The simulation begins at a low-energy ‘reference’ state which is previously found by annealing, and studies how the system diffuses away from this configuration. The local energy minimum configurations reached in time t during the relaxation at temperature T are analyzed by identifying all the connected clusters of spins which have reversed their initial orientation. In particular, the growth of the average cluster volume is examined. The second approach, which is due to Huse, considers the way in which two replicas of the systems approach a low-energy configuration starting from random and uncorrelated high-energy states. Their time coarse grained magnetizations are compared, yielding a measure of the linear cluster size, again as a function of t and T. All our low-temperature data can be scaled on a master curve, whose abscissa b(t, T) is the line in the t, T plane corresponding to constant cluster volume. The region in which this parametrization exists corresponds to the usual thermodynamical low T phases in 3 and 4D. Within the region the form of the growth laws depends on the dimensionality of the system, and on the type of relaxation. For our method we also find a strong and systematic dependence of the growth laws on the annealing time spent to identify the reference state, which is akin to the aging dependence of the linear response: the longer the annealing time, the slower is the growth.