arXiv subjects

M. Dančo

Publications and source records attributed to M. Dančo.

4 recordsLinked to original sources

arXiv2016

Renormalization group calculation of dynamic exponent in the models E and F with hydrodynamic fluctuations

The renormalization group method is applied in order to analyze models E and F of critical dynamics in the presence of velocity fluctuations generated by the stochastic Navier-Stokes equation. Results are given to the one-loop approximation for the anomalous dimension $γ_λ$ and fixed-points' structure. The dynamic exponent $z$ is calculated in the turbulent regime and stability of the fixed points for the standard model E is discussed.

cond-mat.stat-mech↗

arXiv2016

Influence of Hydrodynamic Fluctuations on the Phase Transition in Models E and F of Critical Dynamics

We use the renormalization group method to study model E of critical dynamics in the presence of velocity fluctuations arising in accordance with the stochastic Navier-Stokes equation. Using Martin-Siggia-Rose theorem, we obtain a field- theoretical 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 $\varepsilon$ and $δ$ to calculate renormalization constants. Here, $\varepsilon$ is a deviation from the critical dimension four, and $δ$ is a 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.

cond-mat.stat-mech↗

arXiv2015

Superfluid Phase Transition with Activated Velocity Fluctuations: Renormalization Group Approach

A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within perturbative renormal- ization group method. The double $(ε,δ)$-expansion scheme is employed, where is a deviation from space dimension $4$ and $δ$ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value $4/3$.

cond-mat.stat-mech↗

arXiv2013

Critical Behavior of Percolation Process Influenced by Random Velocity Field: One-Loop Approximation

Using perturbative renormalization group we investigate the influence of random velocity field on the critical behavior of directed bond percolation process near its second-order phase transition between absorbing and active phase. Antonov-Kraichnan model with finite correlation time is used for description of advecting velocity field. The field-theoretic renormalization group approach is applied for getting information about asymptotic large scale behavior of the model under consideration. The model is analyzed near its critical dimension through three-parameter expansion in ε, δ, η, where ε is the deviation from the Kolmogorov scaling, δ is the deviation from the critical space dimension {d_c} and η is the deviation from the parabolic dispersion law for the velocity correlator. Fixed points with corresponding regions of stability are determined to the leading order in the perturbation scheme.

nlin.CD↗