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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
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.
Received: 14.12.2018 Revised: 24.02.2019
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
Linking options:
https://www.mathnet.ru/eng/tmf9680https://doi.org/10.4213/tmf9680 https://www.mathnet.ru/eng/tmf/v200/i3/p478
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Abstract page: | 221 | Full-text PDF : | 28 | References: | 18 | First page: | 5 |
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