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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.
We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known kinetic equa
Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations. As prototypes we study three variants of a generic time-fr
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of these equation
The massive field-theory approach for studying critical behavior in fixed space dimensions $d<4$ is extended to systems with surfaces.This enables one to study surface critical behavior directly in dimensions $d<4$ without having to resort to the $ep
In this study, we analytically formulated the path integral representation of the conditional probabilities for non-Markovian kinetic processes in terms of the free energy of the thermodynamic system. We carry out analytically the time-fractional kin