Fixed-dimension renormalization group analysis of conserved surface roughening

Disorders can induce continuously varying universal scaling in driven systems

We elucidate the nature of universal scaling in a class of quenched disordered driven models. In particular, we 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 having distributions with pertinent structures. We show that when the disorder is relevant in the renormalization group sense, the scaling exponents can depend continuously on a dimensionless parameter that defines the disorder distribution. This result is generic and holds for quenched disorders with or without spatially long-ranged correlations, as long as the disorder remains a "relevant perturbation" on the pure system in the renormalization group sense and a dimensionless parameter naturally exists in its distribution. We speculate on its implications for generic driven systems with quenched disorders, and we compare and contrast with the scaling displayed in the presence of annealed disorders.

Renormalization group study of the dynamics of active membranes: Universality classes and scaling laws

Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.