Intrinsic noise-induced phase transitions: beyond the noise interpretation

TL;DR

This paper investigates intrinsic noise effects in stochastic PDEs, revealing noise-induced phase transitions that occur under both Ito and Stratonovich interpretations, challenging previous assumptions about the necessity of linear instability.

Contribution

It introduces a model exhibiting noise-induced ordering transitions under both noise interpretations, and compares its dynamics with a Ginzburg-Landau model and new numerical algorithms.

Findings

Noise-induced phase transitions occur under both Ito and Stratonovich interpretations.

The model lacks linear instability at the transition point.

Numerical algorithms for both interpretations are developed and discussed.

Abstract

We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Ito vs. Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Ito. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau type model. A detailed discussion of new numerical algorithms used in both interpretations is also presented.