Anomalous Dimension in a Two-Species Reaction–Diffusion System
We study a two-species reaction–diffusion system with the reactions and , with general diffusion constants D A and D B . Previous studies showed that for dimensions the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling , where the exponent results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in , a calculation that involves 61 Feynman diagrams, and also determine the logarithmic corrections at the upper critical dimension . Finally, we determine the exponent numerically utilizing a mapping to a four-walker problem for the special case of A particle coalescence in one spatial dimension.
Journal of Physics A: Mathematical and Theoretical
Physics & Astronomy
Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R Scott; and Hellerick, Joshua D.. "Anomalous Dimension in a Two-Species Reaction–Diffusion System." Journal of Physics A: Mathematical and Theoretical (2017) : 034002-034018.