Disorders can induce continuously varying universal scaling in driven systems

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.

arXiv comment8 Figures, Published 3 March 2022

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• Active XY model on a substrate: Density fluctuations and phase ordering
• Renormalization group analysis of a self-organized critical system: Intrinsic anisotropy vs random environment
• Logarithmic or algebraic: roughening of an active Kardar-Parisi-Zhang surface