Critical dynamics in systems controlled by fractional kinetic equations

TL;DR

This paper investigates the critical dynamics of systems with anomalous scaling using fractional kinetic equations, demonstrating their renormalizability and scaling behavior near critical points.

Contribution

It introduces a fractional stochastic model with nonlocal action, proves its renormalizability, and establishes scaling behavior in superdiffusive regimes.

Findings

Model is multiplicatively renormalizable.

Gell-Mann-Low function evaluated at one-loop.

Scaling behavior confirmed in epsilon-expansion.

Abstract

The article is devoted to the dynamics of systems with an anomalous scaling near a critical point. The fractional stochastic equation of a Lanvevin type with the $\varphi^3$ nonlinearity is considered. By analogy with the model A the field theoretic model is built, and its propagators are calculated. The nonlocality of the new action functional in the coordinate representation is caused by the involving of the fractional spatial derivative. It is proved that the new model is multiplicatively renormalizable, the Gell-Man-Low function in the one-loop approximation is evaluted. The existence of the scaling behavior in the framework of the $\varepsilon$-expansion for a superdiffusion is established.