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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 200, Number 3, Pages 478–493
DOI: https://doi.org/10.4213/tmf9680 (Mi tmf9680) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Passive advection in a percolation process: Two-loop approximation

S. Birnsteinovaa, M. Gnatichabc, T. Lučivjanskýa, L. Mižišinbc, V. Škultétyd

a Pavol Jozef Šafárik University in Košice, Košice, Slovakia
b Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
c Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia
d Scottish Universities Physics Alliance, The University of Edinburgh, Edinburgh, United Kingdom
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DOI: https://doi.org/10.4213/tmf9680
Abstract: We study an instructive model of the directed percolation process near its second-order phase transition between absorbing and active states. We first express the model as a Langevin equation and then rewrite it in a field theory formulation. Using the Feynman diagram technique and the perturbative renormalization group method, we then analyze the resulting response functional. The percolation process is assumed to occur in an external velocity field, which has an additional effect on the properties of spreading. We use the Kraichnan rapid-change ensemble to generate velocity fluctuations. We obtain the structure of the set of fixed points in the two-loop approximation.
Keywords: directed percolation, renormalization group, multiloop Feynman diagram.
Funding agency Grant number
Ministerstvo Školstva, Vedy, Výskumu a Športu Slovenskej Republiky 1/0345/17
Agentúra na Podporu Výskumu a Vývoja APVV-16-0186
This research was supported by VEGA (Grant No. 1/0345/17 of the Ministry of Education, Science, Research, and Sport of the Slovak Republic) and the Slovak Research and Development Agency (Grant under Contract No. APVV-16-0186).
Received: 14.12.2018
Revised: 24.02.2019
English version:
Theoretical and Mathematical Physics, 2019, Volume 200, Issue 3, Pages 1335–1347
DOI: https://doi.org/10.1134/S0040577919090071
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. Birnsteinova, M. Gnatich, T. Lučivjanský, L. Mižišin, V. Škultéty, “Passive advection in a percolation process: Two-loop approximation”, TMF, 200:3 (2019), 478–493; Theoret. and Math. Phys., 200:3 (2019), 1335–1347
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9680
  • https://www.mathnet.ru/eng/tmf/v200/i3/p478
    • This publication is cited in the following 1 articles:
    1. M. Hnatič, J. Honkonen, T. Lučivjanský, L. Mižišin, “Universality classes of percolation processes: renormalization group approach”, Symmetry, 15:9 (2023), 1696  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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