Finite-dimensional signature of spinodal instability in an athermal hysteretic transition

TL;DR

This study investigates the critical phenomena in disordered athermal systems undergoing hysteretic first-order transitions, revealing how disorder influences critical slowing down and spinodal instability across different dimensions.

Contribution

It demonstrates that disorder suppresses critical slowing down and shows that critical behavior is governed by mean-field spinodal instability, with dimension-dependent scaling exponents.

Findings

Disorder suppresses critical slowing down in finite dimensions.

Scaling exponents increase with disorder strength and stabilize.

Mean-field behavior differs significantly from finite-dimensional cases.

Abstract

We study the off-equilibrium critical phenomena across a hysteretic first-order transition in disordered athermal systems. The study focuses on the zero temperature random field Ising model (ZTRFIM) above the critical disorder for spatial dimensions $d=2,3,$ and $4$. We use Monte Carlo simulations to show that disorder suppresses critical slowing down in phase ordering time for finite-dimensional systems. The dynamic hysteresis scaling, the measure of explicit finite-time scaling, is used to subsequently quantify the critical slowing down. The scaling exponents in all dimensions increase with disorder strength and finally reach a stable value where the transformation is no longer critical. The associated critical behavior in the mean-field limit is very different, where the exponent values for various disorders in all dimensions are similar. The non-mean-field exponents asymptotically approach the mean-field value ($\Upsilon \approx 2/3$) with increase in dimensions. The results suggest that the critical features in the hysteretic metastable phase are controlled by inherent mean-field spinodal instability that gets blurred by disorder in low-dimension athermal systems.