Non-universal non-equilibrium critical dynamics with disorder

TL;DR

This paper studies how disorder affects the critical dynamics of one-dimensional reaction-diffusion systems, revealing nonuniversal scaling behaviors through numerical and analytical methods.

Contribution

It introduces combined numerical and analytical approaches to analyze disorder-induced nonuniversal critical dynamics in one-dimensional systems.

Findings

Dynamic exponents are nonuniversal and depend on disorder realizations.

Scaling forms are stretched exponential for specific disorder configurations.

Numerical and analytical results are consistent with each other.

Abstract

We investigate finite size scaling aspects of disorder reaction-diffusion processes in one dimension utilizing both numerical and analytical approaches. The former averages the spectrum gap of the associated evolution operators by doubling their degrees of freedom, while the latter uses various techniques to map the equations of motion to a first passage time process. Both approaches are consistent with nonuniversal dynamic exponents, and with stretched exponential scaling forms for particular disorder realizations.