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Journal of Physics A Mathematical and General

Dynamics in a dilute ferromagnet at the percolation threshold

V. B. Andreǐchenko, Walter Selke, A. L. Talapov

Published Mar 21, 1992• 11 citations
Publisher

Abstract

The dynamics of the spin autocorrelation function and the relaxation of the magnetization in the Griffiths phase of the two-dimensional bond-diluted Ising model at the percolation threshold are studied using Monte Carlo techniques. The results resolve a previous ambiguity about the decay law.
DOI
10.1088/0305-4470/25/6/003

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Europhysics Letters (EPL)•Jan 20, 1995•16 citations
The authors examine the dynamical properties of the 2D+or-J Edwards-Anderson Ising spin glass in the anomalous phase which corresponds to the Griffiths phase in the diluted ferromagnetic system. By using Monte Carlo simulation they find that the autocorrelation function can be described as a function of a power of scaled time. This new scaling includes both the stretched exponential law for the intermediate stage and the logarithmic law for the early stage of relaxation. The relaxation time obtained from the scaling is found to diverge exponentially with exponent proportional to T -2 .
Relaxation phenomena are studied for the ± J Ising spin glass in two dimensions by Monte Carlo method. For each spin, a representative relaxation time of the spin is estimated from the equilibrium autocorrelation function of the spin. Clusters of slowly relaxing spins are found to exist below the critical temperature of the nonrandom Ising ferromagnet. It is also found that the distribution of the relaxation times of spins is consistent with the prediction of the theory which assumes independent motion of clusters. This distribution explains the nonexponential decay of the averaged spin autocorrelation function as in the case of the diluted Ising ferromagnets.
The critical relaxation of the magnetization in a 2D Ising model with quenched random non-magnetic impurities is studied by numerical simulation. A square lattice of size 400 2 and spin concentrations p = 1.0, 0.95, 0.9, 0.85, 0.8, 0.75 and 0.7 are considered. The dynamical critical exponent z is determined by the dynamical renormalization group Monte Carlo method. The values for z(p) are: z (1) = 2.24 ± 0.07, z (0.95) = 2.24 ± 0.06, z (0.9) = 2.24 ± 0.06, z (0.85) = 2.38 ± 0.05, z (0.8) = 2.51 ± 0.06, z (0.75) = 2.66 ± 0.07 and z (0.7) = 2.88 ± 0.06. A singular dynamic-scaling behaviour with z(p) = A '|ln( p − p c )| + B ' is found for systems with spin concentrations near the percolation threshold p c , where A ' = 0.56 ± 0.07 and B ' = 1.62 ± 0.07 are temperature-independent constants.