Eur. Phys. J. B (2018) 91: 269
https://doi.org/10.1140/epjb/e2018-90308-1

Regular Article

Scaling behavior in interacting systems: joint effect of anisotropy and compressibility

¹ Faculty of Science, Šafárik University, Moyzesova 16, 040 01 Košice, Slovakia
² Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
³ Department of Theoretical Physics, St. Petersburg State University, Ulyanovskaya 1, 198504 St. Petersburg, Petrodvorets, Russia

^a e-mail: tomas.lucivjansky@upjs.sk

Received: 2 May 2018
Received in final form: 10 August 2018
Published online: 1 November 2018

Abstract

Motivated by the ubiquity of turbulent flows in realistic conditions, effects of turbulent advection on two models of classical non-linear systems are investigated. In particular, we analyze model A (according to the Hohenberg–Halperin classification [P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)]) of a non-conserved order parameter and a model of the direct bond percolation process. Having two paradigmatic representatives of distinct stochastic dynamics, our aim is to elucidate to what extent velocity fluctuations affect their scaling behavior. The main emphasis is put on an interplay between anisotropy and compressibility of the velocity flow on their respective scaling regimes. Velocity fluctuations are generated by means of the Kraichnan rapid-change model, in which the anisotropy is due to a distinguished spatial direction n and a correlator of the velocity field obeys the Gaussian distribution law with prescribed statistical properties. As the main theoretical tool, the field-theoretic perturbative renormalization group is adopted. Actual calculations are performed in the leading (one-loop) approximation. Having obtained infrared stable asymptotic regimes, we have found four possible candidates for macroscopically observable behavior for each model. In contrast to the isotropic case, anisotropy brings about enhancement of non-linearities and non-trivial regimes are proved to be more stable.