On the nature of different types of absorbing states

TL;DR

This paper compares three Langevin equations with absorbing states, revealing how different noise types influence the physical mechanisms and the nature of absorbing states, with implications for reaction-diffusion models.

Contribution

It provides a comparative analysis of three Langevin equations with absorbing states, highlighting the impact of noise type on physical mechanisms and model universality.

Findings

Different noise types correspond to distinct physical mechanisms.

Multiplicative noise class cannot represent certain reaction-diffusion models.

Complex noise may be necessary to describe specific annihilation processes.

Abstract

We present a comparison of three different types of Langevin equation exhibiting absorbing states: the Langevin equation defining the Reggeon field theory, one with multiplicative noise, and a third type in which the noise is complex. Each one is found to describe a different underlying physical mechanism; in particular, the nature of the different absorbing states depends on the type of noise considered. By studying the stationary single-site effective potential, we analyze the impossibility of finding a reaction-diffusion model in the multiplicative noise universality class. We also discuss some theoretical questions related to the nature of complex noise, as for example, whether it is necessary or not to consider a complex equation in order to describe processes as the annihilation reaction, $A +A \to 0$.