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

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 $d_s\to d_{\mathrm{eff}}=d_s-y$ and thus modifies the divergence structure of loop integrals ($d_s$ is the dimension of space). The model is renormalizable at one-loop for $d_{\mathrm{eff}}<6$ and nonrenormalizable for $d_{\mathrm{eff}}\ge 6$. 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.

8 pages, 7 figures

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