Persistence in the zero-temperature dynamics of the diluted Ising ferromagnet in two dimensions.
The nonequilibrium dynamics of the strongly diluted random-bond Ising model in two dimensions (2D) is investigated numerically. The persistence probability, P(t), of spins which do not flip by time t is found to decay to a nonzero, dilution-dependent value P(infinity). We find that p(t)=P(t)-P(infinity) decays exponentially to zero at large times. Furthermore, the fraction of spins which never flip is a monotonically increasing function over the range of bond-dilution considered. Our findings, which are consistent with a recent result of Newman and Stein [Phys. Rev. Lett. 82, 3944 (1999)], suggest that persistence in diluted and pure systems falls into different classes. Furthermore, its behavior would also appear to depend crucially on the strength of the dilution present.
Jain
S
S
School of Mathematics and Computing, University of Derby, Kedleston Road, Derby DE22 1GB, United Kingdom. S.Jain@derby.ac.uk