Slow Dynamics in the \lsquo Griffiths Phase' of the Two-Dimensional Ising Spin Glass

Abstract

Slow dynamics in the ± J Ising model on a square lattice is studiedby means of Monte Carlo simulation, in which the distribution functionof (logarithms of) relaxation times, P(x) with x=ln τ, isobtained by analyzing individual spin auto-correlation functions oneby one. At each temperature in the \lsquo Griffiths phase', namely inthe range above the spin-glass transition temperature T_c (=0) butbelow the Curie temperature of the corresponding pure ferromagnetTpurec, P(x) exhibits a characteristic crossover behavior at aroundx_c(=ln τ _c) which diverges toward T_c. Thecontributionsto the branch x ≤ x_c are interpreted due to the ordinary criticalslowing down process associated with T_c (critical dynamics). Thebehavior of P(x) at x≤ x_c, on the other hand, is quite consistentwith the picture of relaxation processes of large, rare clustersrelated to the expected Griffiths singularity at Tpurec (clusterdynamics).