Nonequilibrium transitions induced by multiplicative noise

TL;DR

This paper introduces a simple model demonstrating noise-induced ordering and disordering transitions driven by purely multiplicative noise, with analytical and numerical analysis revealing their critical behavior and universality class in one and two dimensions.

Contribution

It presents the first report of noise-induced transitions in one dimension and provides critical exponents for these transitions in 1D and 2D.

Findings

Identification of noise-induced ordering and disordering transitions

Critical exponents computed for 1D and 2D cases

Transitions belong to the multiplicative noise universality class

Abstract

A new simple model exhibiting a noise-induced ordering transition (NIOT) and a noise-induced disordering transition (NIDT), in which the noise is purely multiplicative, is presented. Both transitions are found in two as well as in one dimension (where they had not been previously reported). We show analytically and numerically that the critical behavior of these two transitions is described by the so called multiplicative noise(MN) universality class. A computation of the set of critical exponents is presented in both $d=1$, and $d=2$ (where they have not been previously measured).