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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2013_176_1_a6,
     author = {M. Dan\v{c}o and M. Gnatich and M. V. Komarova and D. M. Krasnov and T. Lu\v{c}ivjansk\'y and L. Mi\v{z}i\v{s}in and M. Yu. Nalimov},
     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},
     publisher = {mathdoc},
     volume = {176},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_176_1_a6/}
}
TY  - JOUR
AU  - M. Dančo
AU  - M. Gnatich
AU  - M. V. Komarova
AU  - D. M. Krasnov
AU  - T. Lučivjanský
AU  - L. Mižišin
AU  - M. Yu. Nalimov
TI  - Influence of hydrodynamic fluctuations on the~phase transition in the~$E$ and $F$ models of critical dynamics
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2013
SP  - 69
EP  - 78
VL  - 176
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2013_176_1_a6/
LA  - ru
ID  - TMF_2013_176_1_a6
ER  - 
%0 Journal Article
%A M. Dančo
%A M. Gnatich
%A M. V. Komarova
%A D. M. Krasnov
%A T. Lučivjanský
%A L. Mižišin
%A M. Yu. Nalimov
%T Influence of hydrodynamic fluctuations on the~phase transition in the~$E$ and $F$ models of critical dynamics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2013
%P 69-78
%V 176
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2013_176_1_a6/
%G ru
%F TMF_2013_176_1_a6
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/