Dynamic scaling in the quenched disordered classical $N$-vector model

TL;DR

This paper investigates how short-range quenched disorder affects the universal dynamic scaling properties of the classical N-vector model with cubic anisotropy, revealing slower dynamics and potential breakdown of scaling near critical points.

Contribution

It introduces a one-loop dynamic renormalisation group analysis of the model, showing disorder-induced slowing down and a thresholdless instability affecting universality classes.

Findings

Disorder generally slows down the dynamics near critical points.

Quenched disorder can cause a breakdown of dynamic scaling.

Potential for a disorder-induced first order transition.

Abstract

We revisit the effects of short-ranged random quenched disorder on the universal scaling properties of the classical $N$-vector model with cubic anisotropy. We set up the nonconserved relaxational dynamics of the model, and study the universal dynamic scaling near the second order phase transition. We extract the critical exponents and the dynamic exponent in a one-loop dynamic renormalisation group calculation with short-ranged isotropic disorder. We show that the dynamics near a critical point is generically slower when the quenched disorder is relevant than when it is not, independent of whether the pure model is isotropic or cubic anisotropic. We demonstrate the surprising thresholdless instability of the associated universality class due to perturbations from rotational invariance breaking quenched disorder-order parameter coupling, indicating breakdown of dynamic scaling. We speculate that this may imply a novel first order transition in the model, induced by a symmetry-breaking disorder.