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This article is cited in 3 scientific papers (total in 3 papers)
Influence of hydrodynamic fluctuations on the phase transition in the $E$ and $F$ models of critical dynamics
M. Dančoa, M. Gnatichb, M. V. Komarovac, D. M. Krasnovc, T. Lučivjanskýab, L. Mižišinb, M. Yu. Nalimovc a Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia
b Faculty of Science, P. J. Šafárik University, Košice, Slovakia
c Saint Petersburg State University, St. Petersburg, Russia
Abstract:
We use the renormalization group method to study the $E$ model of critical dynamics in the presence of velocity fluctuations arising in accordance with the stochastic Navier–Stokes equation. Using the Martin–Siggia–Rose theorem, we obtain a field theory model that allows a perturbative renormalization group analysis. By direct power counting and an analysis of ultraviolet divergences, we show that the model is multiplicatively renormalizable, and we use a two-parameter expansion in $\epsilon$ and $\delta$ to calculate the renormalization constants. Here, $\epsilon$ is the deviation from the critical dimension four, and $\delta$ is the deviation from the Kolmogorov regime. We present the results of the one-loop approximation and part of the fixed-point structure. We briefly discuss the possible effect of velocity fluctuations on the large-scale behavior of the model.
Keywords:
Bose condensation, $F$ model, renormalization group, anomalous scaling exponent, critical dynamics.
Received: 19.12.2012 Revised: 05.03.2013
Citation:
M. Dančo, M. Gnatich, M. V. Komarova, D. M. Krasnov, T. Lučivjanský, L. Mižišin, M. Yu. Nalimov, “Influence of hydrodynamic fluctuations on the phase transition in the $E$ and $F$ models of critical dynamics”, TMF, 176:1 (2013), 69–78; Theoret. and Math. Phys., 176:1 (2013), 888–897
Linking options:
https://www.mathnet.ru/eng/tmf8479https://doi.org/10.4213/tmf8479 https://www.mathnet.ru/eng/tmf/v176/i1/p69
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Abstract page: | 379 | Full-text PDF : | 162 | References: | 63 | First page: | 31 |
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