Searcharxiv⌕ Search

arXiv subjects

T. Lučivjanský

Publications and source records attributed to T. Lučivjanský.

29 records · Page 2Linked to original sources
arXiv2016

Numerical calculation of scaling exponents of percolation process in the framework of renormalization group approach

We use the renormalization group theory to study the directed bond percolation (Gribov process) near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the $ε$-expansion where $ε$ is a deviation from the upper critical dimension $d_c = 4$. Within this procedure anomalous dimensions $γ$ are expressed in terms of irreducible renormalized Feynman diagrams and thus the calculation of renormalization constants could be entirely skipped. The renormalization group is included by means of the $R$ operation, and for computational purposes we choose the null momentum subtraction scheme.

cond-mat.stat-mech↗
arXiv2016

Directed percolation process in the presence of velocity fluctuations: Effect of compressibility and finite correlation time

The direct bond percolation process (Gribov process) is studied in the presence of random velocity fluctuations generated by the Gaussian self-similar ensemble with finite correlation time. We employ the renormalization group in order to analyze a combined effect of the compressibility and finite correlation time on the long-time behavior of the phase transition between an active and an absorbing state. The renormalization procedure is performed to the one-loop order. Stable fixed points of the renormalization group and their regions of stability are calculated in the one-loop approximation within the three-parameter $(\eps,y,η)$-expansion. Different regimes corresponding to the rapid-change limit and frozen velocity field are discussed, and their fixed points' structure is determined in numerical fashion.

cond-mat.stat-mech↗
arXiv2015

Directed Percolation Process Advected by Compressible Velocity Field

The directed percolation process in the vicinity of non-equilibrium phase transition is studied by the means of field theoretic methods. It will be assumed that percolation takes place in a compressible environment, which will be generated by the modified Kraichnan model. We will discuss differ- ences with the incompressible case and describe how the given model can be renormalized. The renormalization constants will be given to the one-loop order.

nlin.CD↗
arXiv2015

Tricritical Properties of Antiferromagnetic Ising Model on the Square Lattice

The Ising square lattice model with nearest-neighbor (nn) interactions ($J_1$) is one of the few exactly solvable models [1]. Adding next-neareast- neighbor (nnn) interactions ($J_2$) or a magnetic field (or both) leads to the non solvability of the model and only some approximate solutions are possible. In this brief report we will review some results obtained within effective field theory. We will show that besides second-order transitions there are also lines of first-order transitions and the coordinates of tricritical points are calculated.

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↗
arXiv2015

Phase transitions in a frustrated Ising antiferromagnet on a square lattice

The phase transitions occurring in the frustrated Ising square antiferromagnet with first- ($J_1 < 0$) and second- ($J_2 < 0$) nearest-neighbor interactions are studied within the framework of the effective-field theory with correlations based on the different cluster sizes and for a wide range of $R = J_2/|J_1|$. Despite the simplicity of the model, it has proved difficult to precisely determine the order of the phase transitions. In contrast to the previous effective-field study, we have found a first-order transition line in the region close to $R = -0.5$ not only between the superantiferromagnetic and paramagnetic ($R<-0.5$) but also between antiferromagnetic and paramagnetic ($R>-0.5$) phases.

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↗
arXiv2012

Critical Behaviour Of Directed Percolation In The Presence Of Synthetic Velocity Field

Using perturbative renormalization group we study the influence of random velocity field on the critical behaviour of directed bond percolation process near its second-order phase transition between absorbing and active phase. We consider Kraichnan model with finite correlation time for modelling advecting velocity field. Using functional integral representation we are able to apply field-theoretic renormalization group to determine possible universality classes. The model is analyzed near its critical dimension by means of three-parameter expansion in $ε,δ,η$, where $ε$ is the deviation from the Kolmogorov scaling, $δ$ 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 evaluated to the leading order in the perturbation scheme.

nlin.CD↗
arXiv2011

Study of Anomalous Kinetics of The Annihilation Reaction A+A->0

Using the perturbative renormalization group, we study the influence of a random velocity field on the kinetics of the single-species annihilation reaction A+A->0 at and below its critical dimension d_c=2. We use the second-quantization formalism of Doi to bring the stochastic problem to a field-theoretic form. We investigate the reaction in the vicinity of the space dimension d=2 using a two-parameter expansion in $ε$ and $Δ$, where $ε$ is the deviation from the Kolmogorov scaling parameter and $Δ$ is the deviation from the space dimension d=2. We evaluate all the necessary quantities, including fixed points with their regions of stability, up to the second order of the perturbation theory.

nlin.CD↗
arXiv2011

Field Theory Approach In Kinetic Reaction: Role Of Random Sources And Sinks

In the framework of a field theoretic model obtained by second quantization of Doi-type master equation, we investigate the effects of random sources and sinks on the reaction kinetics in the master-equation description. We show that random sources and sinks significantly affect the asymptotic behavior of the model and identify two universality classes when describing them using scaling analysis. We compare the results with the Langevin-equation description of the same process.

cond-mat.stat-mech↗