Spinodals with Disorder: from Avalanches in Random Magnets to Glassy Dynamics

TL;DR

This paper develops a rigorous theory for spinodals in disordered systems, revealing critical behavior characterized by exponential divergence and mild nonanalyticities, with implications for understanding glassy dynamics.

Contribution

It provides a complete, zero-temperature theory of spinodals in the RFIM, highlighting differences from mean-field predictions and connecting to glassy dynamics.

Findings

Spinodal criticality involves depinning and droplet expansion.

Characteristic length diverges exponentially in finite dimensions.

Thermodynamic nonanalyticities are mild, akin to Griffith phenomena.

Abstract

We revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. We focus on the spinodal of an Ising model in a quenched random field (RFIM), which has applications in many areas from materials to social science. By working at zero temperature in the quasi-statically driven RFIM, thermal fluctuations are eliminated and one can give a rigorous content to the notion of spinodal. We show that the latter is due to the depinning and the subsequent expansion of rare droplets. We work out the associated critical behavior, which, in any finite dimension, is very different from the mean-field one: the characteristic length diverges exponentially and the thermodynamic quantities display very mild nonanalyticities much like in a Griffith phenomenon. From the recently established connection between the spinodal of the RFIM and glassy dynamics, our results also allow us to conclusively assess the physical content and the status of the dynamical transition predicted by the mean-field theory of glass-forming liquids.