Disorders can induce continuously varying universal scaling in driven systems

TL;DR

This paper investigates how quenched disorder influences universal scaling in driven systems, revealing that relevant disorder can cause continuous variation in scaling exponents, with implications for a broad class of models.

Contribution

It demonstrates that relevant quenched disorder can lead to continuously varying universality classes in driven systems, extending the understanding of disorder effects in non-equilibrium models.

Findings

Disorder relevance affects scaling exponents.

Scaling exponents can vary continuously with disorder parameters.

Results apply to disorders with or without spatial correlations.

Abstract

We elucidate the nature of universal scaling in disordered driven models. We in particularly explore the intriguing possibility of whether coupling with quenched disorders can lead to continuously varying universality classes. We examine this question in the context of the Kardar-Parisi-Zhang (KPZ) equation, with and without a conservation law, coupled with quenched disorders of appropriate structures. By using a renormalisation group (RG) framework, we show when the disorder is relevant in the RG sense, the scaling exponents can depend continuously on a dimensionless parameter that defines the disorder variance. This result is generic and holds for quenched disorders with or without spatially long ranged correlations, as long as the disorder remains "relevant perturbation" on the pure system in a renormalisation group sense and a dimensionless parameter naturally exists in its variance. We speculate on its implications for generic driven systems with quenched disorders, and compare and contrast with the scaling displayed in the presence of annealed disorders.