Abstract
In this work we focus on two-species reaction-diffusion system involving two reaction processes \(A + A \to (\emptyset ,A)\) , and \(A + B \to A\) . Reactants are subject to diffusive spreading with arbitrary diffusion constants. Such a system was studied earlier at and below its upper critical dimension \({{d}_{{\text{c}}}} = 2\) in [2, 3], and recently also in the presence of long-range spreading with fractional Laplace operator \({{\partial }^{\sigma }} \equiv {{\partial }^{{2(1 - \alpha )}}}\) [5–7]. In the latter case, however, only long-range limit was explored ( \(\alpha \gg \epsilon \) ), where \(\epsilon = {{d}_{{\text{c}}}} - d = 2 - d\) . Here, our aim is to investigate the hybrid regime in which parameters α and \(\epsilon \) are of the same order, i.e. \(\alpha = O(\epsilon )\) . Our primary theoretical tool is field-theoretic perturbative renormalization group augmented with the approach of Honkonen and Nalimov [8]. The model is renormalized to all orders of perturbation theory, stable long-time asymptotic regimes are identified and time-decay exponent of respective particle densities is calculated.
