Geodesic
Influence of hydrodynamic fluctuations on the phase transition in the $E$ and $F$ models of critical dynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 1, pp. 69-78 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : Bose condensation
Keywords: $F$ model, renormalization group, anomalous scaling exponent, critical dynamics. 
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     title = {Influence of hydrodynamic fluctuations on the~phase transition in the~$E$ and $F$ models of critical dynamics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {69--78},
     year = {2013},
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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. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 1, pp. 69-78. http://geodesic.mathdoc.fr/item/TMF_2013_176_1_a6/

[1] A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinskii, Metody kvantovoi teorii polya v statisticheskoi fizike, Dobrosvet, M., 2006 | MR | Zbl

[2] P. C. Hohenberg, B. I. Halperin, Rev. Modern Phys., 49:3 (1977), 435–479 | DOI

[3] C. De Dominicis, L. Peliti, Phys. Rev. B, 18:1 (1978), 353–376 | DOI

[4] M. V. Komarova, D. M. Krasnov, M. Yu. Nalimov, TMF, 169:1 (2011), 89–99 | DOI | DOI | Zbl

[5] J. Honkonen, M. Yu. Nalimov, J. Phys. A, 22:6 (1989), 751–763 | DOI

[6] J. Honkonen, M. Yu. Nalimov, Z. Phys. B, 99:2 (1996), 297–303 | DOI

[7] N. V. Antonov, M. Hnatic, J. Honkonen, J. Phys. A, 39:25 (2006), 7867–7887 | DOI | MR | Zbl

[8] P. C. Martin, E. D. Siggia, H. A. Rose, Phys. Rev. A, 8:1 (1973), 423–437 | DOI

[9] J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, International Series of Monographs on Physics, 85, Clarendon Press, Oxford, 1996 | MR

[10] A. N. Vasilev, Funktsionalnye metody v kvantovoi teorii polya i statistike, Izd-vo LGU, L., 1976

[11] A. N. Vasilev, Kvantovopolevaya renormgruppa v teorii kriticheskogo povedeniya i stokhasticheskoi dinamike, Izd-vo PIYaF, SPb., 1998 | MR