Persistence and the Random Bond Ising Model in Two Dimensions

TL;DR

This study investigates zero-temperature persistence in the 2D random bond ±J Ising model, revealing non-monotonic behavior, a spin glass transition, and an algebraic decay of residual persistence with a consistent exponent.

Contribution

It provides extensive numerical evidence for persistent blocking and characterizes the non-monotonic persistence behavior across different disorder levels in the 2D random bond Ising model.

Findings

Persistence fraction shows non-monotonic, double-humped behavior.

Residual persistence decays algebraically with exponent ~0.9.

Model exhibits mixed behavior with finite and infinite flip spins.

Abstract

We study the zero-temperature persistence phenomenon in the random bond $\pm J$ Ising model on a square lattice via extensive numerical simulations. We find strong evidence for ` blocking\rq regardless of the amount disorder present in the system. The fraction of spins which {\it never} flips displays interesting non-monotonic, double-humped behaviour as the concentration of ferromagnetic bonds $p$ is varied from zero to one. The peak is identified with the onset of the zero-temperature spin glass transition in the model. The residual persistence is found to decay algebraically and the persistence exponent $\theta (p)\approx 0.9$ over the range $0.1\le p\le 0.9$. Our results are completely consistent with the result of Gandolfi, Newman and Stein for infinite systems that this model has ` mixed\rq behaviour, namely positive fractions of spins that flip finitely and infinitely often, respectively. [Gandolfi, Newman and Stein, Commun. Math. Phys. {\bf 214} 373, (2000).]