Persistence in the Zero-Temperature Dynamics of the Diluted Ising Ferromagnet in Two Dimensions

TL;DR

This study numerically investigates the zero-temperature dynamics of a diluted 2D Ising ferromagnet, revealing that spin persistence decays to a dilution-dependent non-zero value and that the dynamics differ from pure systems.

Contribution

It provides new insights into the persistence behavior in diluted disordered systems, showing exponential decay and dilution-dependent non-zero limits, contrasting with pure systems.

Findings

Persistence probability approaches a non-zero limit depending on dilution

Decay of P(t) - P(∞) is exponential at large times

Fraction of non-flipping spins increases with dilution

Abstract

The non-equilibrium 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 non-zero, dilution-dependent, value $P(\infty)$. We find that $p(t)=P(t)-P(\infty)$ 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, suggest that persistence in disordered and pure systems falls into different classes. Furthermore, its behaviour would also appear to depend crucially on the strength of the dilution present.