Multiplicative Noise in Non-equilibrium Phase Transitions: A tutorial

TL;DR

This tutorial reviews the role of multiplicative noise in non-equilibrium phase transitions across various fields, focusing on universality classes and physical realizations.

Contribution

It classifies universality classes of non-equilibrium phase transitions with multiplicative noise and discusses multiple physical systems exhibiting these phenomena.

Findings

Classification of universality classes for multiplicative noise transitions

Analysis of physical systems like depinning and wetting phenomena

Insights into synchronization and other non-equilibrium behaviors

Abstract

Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of spatially extended systems with this type of stochasticity, paying special attention to the {\it non-equilibrium phase transitions} these systems may exhibit, are reviewed here. In particular we study and classify the possible universality classes of such transitions, and discuss some specific physical realizations including depinning transitions of non-equilibrium interfaces, non-equilibrium wetting phenomena, synchronization of spatially extended systems and many others.