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

TL;DR

This study investigates the slow relaxation dynamics of the bond-diluted 2D Ising model below the percolation threshold, revealing stretched exponential decay behavior with temperature-dependent exponents using Monte Carlo simulations.

Contribution

It demonstrates that both magnetization decay and autocorrelation follow a stretched exponential law with a bond concentration-independent exponent.

Findings

Relaxation follows a stretched exponential form.

Exponent depends on temperature but not on bond concentration.

Asymptotic regime not reached even at very low correlation values.

Abstract

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}.