Integration of Langevin Equations with Multiplicative Noise and Viability of Field Theories for Absorbing Phase Transitions

TL;DR

This paper presents a split-step scheme for integrating stochastic differential equations with multiplicative noise, demonstrating its effectiveness in studying absorbing phase transitions and clarifying their theoretical classification.

Contribution

The paper introduces a split-step integration method that accurately solves Langevin equations with multiplicative noise, improving analysis of absorbing phase transitions.

Findings

Provides precise estimates of scaling exponents for absorbing phase transitions

Clarifies the classification of nonequilibrium phase transition problems

Confirms or challenges existing theoretical frameworks

Abstract

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic part, the latter being performed by sampling exactly the solution of the associated Fokker-Planck equation. We demonstrate the computational power of this method by applying it to most absorbing phase transitions for which Langevin equations have been proposed. This provides precise estimates of the associated scaling exponents, clarifying the classification of these nonequilibrium problems, and confirms or refutes some existing theories.