Clues on chemical mechanisms from renormalizability: The example of a noisy cubic autocatalytic model

TL;DR

This paper investigates how spatially correlated Gaussian noise influences the renormalizability of a reaction-diffusion model of autocatalytic chemistry, revealing that noise can induce new interactions and alter the model's divergence properties.

Contribution

It demonstrates how noise modifies the divergence structure and renormalizability of a chemical reaction model, and introduces a framework for understanding noise-induced interactions as chemical mechanisms.

Findings

Renormalizability depends on the effective dimension $d_{eff} = d_s - y$.

Noise induces new interaction terms interpreted as chemical mechanisms.

The model is renormalizable for $d_{eff} < 6$ and nonrenormalizable for $d_{eff}  6$.

Abstract

We study the effect of noise on the renormalizability of a specific reaction-diffusion system of equations describing a cubic autocatalytic chemical reaction. The noise we are using is gaussian with power-law correlations in space, characterized by an amplitude $A$ and a noise exponent $y$. We show that changing the noise exponent is equivalent to the substitution $d_{s} \rightarrow d_{\rm eff} = d_{s} - y$ and thus modifies the divergence structure of loop integrals ($d_{s}$ is the dimension of space). The model is renormalizable at one-loop for $d_{\rm eff} < 6$ and nonrenormalizable for $d_{\rm eff} \geq 6$. The effects of noise-generated higher order interactions are discussed. In particular, we show how noise induces new interaction terms that can be interpreted as a manifestation of some (internal) "chemical mechanism". We also show how ideas of effective field theory can be applied to construct a more fundamental chemical model for this system.