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