Anomalously slow relaxation in the diluted Ising model below the percolation threshold

Details Anomalously slow relaxation in the diluted Ising model below the percolation threshold Anomalously slow relaxation in the diluted Ising model below the percolation threshold

1995-05-11

arxiv.org/abs/cond-mat/9505044v1

Physics

Condensed Matter

33 pages, including 10 figures, tex; hard-copy available on request from S.Jain@derby.ac.uk To appear in Physica A (Statistica

Scientific paper

The relaxational behaviour of the bond-diluted two-dimensional Ising model below the percolation threshold is studied using Monte Carlo techniques. The non-equilibrium decay of the magnetization,M(t), and the relaxation of the equilibrium spin-spin autocorrelation function, C(t), are monitored. The behaviour of both C(t) and M(t) is found to satisfy the Kohlrausch law of a stretched exponential with the same temperature-dependent exponent. The Kohlrausch exponent does not appear to depend on the bond concentration. The results indicate that we are not yet in the asymptotic regime, even when C(t) and M(t) are less than 10^{-4}.

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