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Directed-bond percolation subjected to synthetic compressible velocity fluctuations: Renormalization group approach

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Abstract

We study the directed-bond percolation process (sometimes called the Gribov process because it formally resembles Reggeon field theory) in the presence of irrotational velocity fluctuations with long-range correlations. We use the renormalization group method to investigate the phase transition between an active and an absorbing state. All calculations are in the one-loop approximation. We calculate stable fixed points of the renormalization group and their regions of stability in the form of expansions in three parameters (ε, y, η). We consider different regimes corresponding to the Kraichnan rapid-change model and a frozen velocity field.

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Author information

Authors and Affiliations

  1. St. Petersburg University, St. Petersburg, Russia

    N. V. Antonov & A. S. Kapustin

  2. Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia

    M. Hnatich

  3. Pavol Jozef Šafárik University in Košice, Košice, Slovakia

    M. Hnatich, T. Lučivjanský & L. Mižišin

  4. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

    M. Hnatich

  5. University of Duisburg-Essen, Essen, Germany

    T. Lučivjanský

Authors
  1. N. V. Antonov
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  2. M. Hnatich
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  3. A. S. Kapustin
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  4. T. Lučivjanský
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  5. L. Mižišin
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Corresponding author

Correspondence to N. V. Antonov.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 190, No. 3, pp. 377–390, March, 2017.

This research was supported by the Ministry of Education, Science, Research, and Sport of the Slovak Republic (VEGA Grant No. 1/0345/17).

The research of N. V. Antonov was supported by St. Petersburg State University (Research Grant No. 11.38.185.2014).

The research of A. S. Kapustin was supported by St. Petersburg State University (Research Grant No. 11.38.185.2014) and the Russian Foundation for Basic Research (Grant No. 16-32-00086).

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Antonov, N.V., Hnatich, M., Kapustin, A.S. et al. Directed-bond percolation subjected to synthetic compressible velocity fluctuations: Renormalization group approach. Theor Math Phys 190, 323–334 (2017). https://doi.org/10.1134/S0040577917030023

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