Kardar-Parisi-Zhang universality class for the critical dynamics of reaction-diffusion fronts

TL;DR

This study numerically investigates the critical dynamics of reaction-diffusion fronts in two dimensions, demonstrating that their fluctuations belong to the KPZ universality class, with new insights into statistical properties of the front.

Contribution

It provides the first detailed numerical analysis of the critical exponents and fluctuation statistics of reaction-diffusion fronts in 2D, confirming KPZ universality.

Findings

Critical exponents match KPZ class predictions.

Front fluctuation statistics are consistent with KPZ universality.

New analysis of one-point statistics and covariance supports universality.

Abstract

We have studied front dynamics for the discrete $A+A \leftrightarrow A$ reaction-diffusion system, which in the continuum is described by the (stochastic) Fisher-Kolmogorov-Petrovsky-Piscunov equation. We have revisited this discrete model in two space dimensions by means of extensive numerical simulations and an improved analysis of the time evolution of the interface separating the stable and unstable phases. In particular, we have measured the full set of critical exponents which characterize the spatio-temporal fluctuations of such front for different lattice sizes, focusing mainly in the front width and correlation length. These exponents are in very good agreement with those computed in [E. Moro, Phys. Rev. Lett. 87, 238303 (2001)] and correspond to those of the Kardar-Parisi-Zhang (KPZ) universality class for one-dimensional interfaces. Furthermore, we have studied the one-point statistics and the covariance of rescaled front fluctuations, which had remained thus far unexplored in the literature and allows for a further stringent test of KPZ universality.