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 TMF, 2011, Volume 169, Number 1, Pages 124–136 (Mi tmf6714)

Effects of turbulent transfer on critical behavior

N. V. Antonov, A. S. Kapustin, A. V. Malyshev

Saint Petersburg State University, St.~Petersburg, Russia

Abstract: Using the field theory renormalization group, we study the critical behavior of two systems subjected to turbulent mixing. The first system, described by the equilibrium model A, corresponds to the relaxational dynamics of a nonconserved order parameter. The second system is the strongly nonequilibrium reaction–diffusion system, known as the Gribov process or directed percolation process. The turbulent mixing is modeled by the stochastic Navier–Stokes equation with a random stirring force with the correlator $\propto\delta(t-t')p^{4-d-y}$, where $p$ is the wave number, $d$ is the space dimension, and $y$ is an arbitrary exponent. We show that the systems exhibit various types of critical behavior depending on the relation between $y$ and $d$. In addition to known regimes (original systems without mixing and a passively advected scalar field), we establish the existence of new strongly nonequilibrium universality classes and calculate the corresponding critical dimensions to the first order of the double expansion in $y$ and $\varepsilon=4-d$ (one-loop approximation).

Keywords: renormalization group, critical behavior, turbulent transfer

DOI: https://doi.org/10.4213/tmf6714

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English version:
Theoretical and Mathematical Physics, 2011, 169:1, 1470–1480

Bibliographic databases:

Citation: N. V. Antonov, A. S. Kapustin, A. V. Malyshev, “Effects of turbulent transfer on critical behavior”, TMF, 169:1 (2011), 124–136; Theoret. and Math. Phys., 169:1 (2011), 1470–1480

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf6714
• https://doi.org/10.4213/tmf6714
• http://mi.mathnet.ru/eng/tmf/v169/i1/p124

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Sarkar N., Basu A., “Active-to-absorbing-state phase transition in the presence of fluctuating environments: Weak and strong dynamic scaling”, Phys. Rev. E, 86:2 (2012), 021122, 13 pp.
2. Antonov N.V. Malyshev A.V., “Effects of turbulent mixing on critical behaviour: renormalization-group analysis of the Potts model”, J. Phys. A, 45:25 (2012), 255004, 21 pp.
3. M. Dančo, M. Gnatich, T. Lučivjanský, L. Mižišin, “Critical behavior of percolation process influenced by a random velocity field: One–loop approximation”, Theoret. and Math. Phys., 176:1 (2013), 898–905
4. Sarkar N., Basu A., “Active To Absorbing State Phase Transition in the Presence of a Fluctuating Environment: Feedback and Universality”, J. Stat. Mech.-Theory Exp., 2014, P08016
5. N. V. Antonov, P. I. Kakin, “Random interface growth in a random environment: Renormalization group analysis of a simple model”, Theoret. and Math. Phys., 185:1 (2015), 1391–1407
6. Sarkar N., “Active-To-Absorbing-State Phase Transition in An Evolving Population With Mutation”, Phys. Rev. E, 92:4 (2015), 042110
7. Antonov N.V. Hnatic M. Kapustin A.S. Lucivjansky T. Mizisin L., “Directed Percolation Process in the Presence of Velocity Fluctuations: Effect of Compressibility and Finite Correlation Time”, Phys. Rev. E, 93:1 (2016), 012151
8. Hnatic M. Honkonen J. Lucivjansky T., “Advanced Field-Theoretical Methods in Stochastic Dynamics and Theory of Developed Turbulence”, Acta Phys. Slovaca, 66:2-3 (2016), 69–265
9. Antonov N.V., Kakin P.I., “Effects of Random Environment on a Self-Organized Critical System: Renormalization Group Analysis of a Continuous Model”, Mathematical Modeling and Computational Physics (MMCP 2015), EPJ Web of Conferences, 108, eds. Adam G., Busa J., Hnatic M., EDP Sciences, 2016, 02009
10. N. V. Antonov, M. Gnatich, A. S. Kapustin, T. Lučivjanský, L. Mižišin, “Directed-bond percolation subjected to synthetic compressible velocity fluctuations: Renormalization group approach”, Theoret. and Math. Phys., 190:3 (2017), 323–334
11. Antonov N.V. Kakin P.I., “Scaling in erosion of landscapes: renormalization group analysis of a model with turbulent mixing”, J. Phys. A-Math. Theor., 50:8 (2017), 085002
12. Antonov N.V. Hnatich M. Kapustin A.S. Lucivjansky T. Mizisin L., “Active-to-Absorbing Phase Transition Subjected to the Velocity Fluctuations in the Frozen Limit Case”, Phys. Part. Nuclei Lett., 14:6 (2017), 944–952
13. Honkonen J. Lucivjansky T. Skultety V., “Influence of Turbulent Mixing on Critical Behavior of Directed Percolation Process: Effect of Compressibility”, Phys. Rev. E, 97:2 (2018), 022123
14. Hnatic M., Kalagov G., Lucivjansky T., “Scaling Behavior in Interacting Systems: Joint Effect of Anisotropy and Compressibility”, Eur. Phys. J. B, 91:11 (2018), 269
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