Zero Temperature Dynamics of the Weakly Disordered Ising Model

TL;DR

This paper investigates the zero-temperature Glauber dynamics of the 2d Ising model with weak disorder, revealing distinct regimes of domain growth and persistence decay, including algebraic and logarithmic behaviors.

Contribution

It provides a detailed analysis of the persistence probability and domain growth regimes in the disordered 2d Ising model at zero temperature, identifying new scaling behaviors.

Findings

Persistence probability decays algebraically in pure case

Three regimes identified in disordered case: pure-like, intermediate, frozen

Intermediate regime shows logarithmic decay of persistence

Abstract

The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that $P(t)\sim L(t)^{-\theta'}$, where $\theta' = 0.420\pm 0.009$. The value of $\theta'$ is consistent with that found for the pure 2d Ising model at zero-temperature. Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, $P(t)\sim (\ln t)^{-\theta_d}$, where $\theta_d = 0.63\pm 0.01$.