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

Abstract

Slow dynamics in the ± J Ising model on a square lattice is studied by means of Monte Carlo simulation, in which the distribution function of (logarithms of) relaxation times, P ( x ) with x =ln τ , is obtained by analyzing individual spin auto-correlation functions one by one. At each temperature in the \lqGriffiths phase', namely in the range above the spin-glass transition temperature T c (=0) but below the Curie temperature of the corresponding pure ferromagnet Tpurec, P ( x ) exhibits a characteristic crossover behavior at around x c (=ln τ c ) which diverges toward T c . The contributions to the branch x ≤ x c are interpreted due to the ordinary critical slowing down process associated with T c (critical dynamics). The behavior of P ( x ) at x ≤ x c , on the other hand, is quite consistent with the picture of relaxation processes of large, rare clusters related to the expected Griffiths singularity at Tpurec (cluster dynamics).