Monte Carlo Study of Griffiths Phase in Randomly Site Diluted Ising Magnetic System

We study the dynamics of spin autocorrelation function and the non-equilibrium decay of magnetization in the Griffiths phase of randomly site diluted Ising magnetic systems by Monte Carlo simulation. The results show that the relaxations are non-exponential for both two- and three-dimensional diluted Ising magnetic systems. At a long timescale, the asymptotic dynamics of the spin autocorrelation function C(t) behaves in the form of C(t) ～ exp-A(ln t)^d/d-1, expected by the theoretical prediction based on clustering arguments. Furthermore we show that the evolution of the spin autocorrelation function satisfies rather well a stretched exponential form of C(t) ～ exp-(t/t)^β even at quite small timescales.