arXiv subjects

Mikhail V. Kompaniets

Publications and source records attributed to Mikhail V. Kompaniets.

7 recordsLinked to original sources

arXiv2026

Dynamic critical exponent of the Yang--Lee edge singularity at three loops

We compute the dynamic critical exponent $z$ of the Yang--Lee edge singularity in relaxational dynamics using perturbative renormalization-group methods to the three-loop order. The calculation combines diagram reduction, analytic two-loop evaluation via parametric integration with hyperlogarithms, and numerical evaluation of three-loop integrals using the Sector Decomposition method. The perturbative series obtained is resummed using Padé and Padé-Borel-Leroy methods to produce estimates of $z$ in various spatial dimensions. The resulting values are consistent with previous perturbative and functional renormalization-group calculations.

cond-mat.stat-mech↗

arXiv2025

Multiloop calculations with parametric integration in critical dynamics: the four-loop analytic study of model A of $ϕ^4$ theory

We perform an analytical four loop calculation of exponent $z$ in model A of critical dynamics in $d=4-2\varepsilon$ dimensions. This is the first time such a large order of perturbation theory has been calculated analytically for models of critical dynamics. To do this, we apply the modern method of parametrical integration with hyperlogaritms. We discuss in detail peculiarities of application of this method to critical dynamics, e.g. the problem of linear-irreducible diagrams already present in four loop (contrary to statics where the first linear-irreducible diagram appears in six loop).

cond-mat.stat-mech↗

arXiv2025

Field-theoretic Analysis of Dynamic Isotropic Percolation: Three-loop Approximation

The general epidemic process is a paradigmatic model in non-equilibrium statistical physics displaying a continuous phase transition between active and absorbing states.The dynamic isotropic percolation universality class captures its universal properties, which we aim to quantitatively study by means of the field-theoretic formulation of the model augmented with a perturbative renormalization group analysis. The main purpose of this work consists in determining the critical dynamic exponent $z$ to the three-loop approximation. This allows us to finalize the quantitative description of the dynamic isotropic percolation class to this order of perturbation theory. The calculations are performed within the dimensional regularization with the minimal subtraction scheme and actual perturbative expansions are carried out in a formally small parameter $ε$, where $ε= 6 - d$ is a deviation from the upper critical dimension $d_c = 6$.

cond-mat.stat-mech↗

arXiv2024

Hyperlogarithms in the theory of turbulence of infinite dimension

Parametric integration with hyperlogarithms so far has been successfully used in problems of high energy physics (HEP) and critical statics. In this work, for the first time, it is applied to a problem of critical dynamics, namely, a stochastic model of developed turbulence in high-dimensional spaces, which has a propagator that is non-standard with respect to the HEP: $(-i ω+ νk^2)^{-1}$. Adaptation of the hyperlogarithm method is carried out by choosing a proper renormalization scheme and considering an effective dimension of the space. Analytical calculation of the renormalization group functions is performed up to the fourth order of the perturbation theory, $\varepsilon$-expansion of the critical exponent $ω$ responsible for the infrared stability of the fixed point is obtained.

cond-mat.stat-mech↗

arXiv2023

Field-theoretic analysis of directed percolation: Three-loop approximation

The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we study this model by means of the field-theoretic formulation with a subsequent renormalization group analysis. We calculate all critical exponents needed for the quantitative description of the corresponding universality class to the third order in perturbation theory. Using dimensional regularization with minimal subtraction scheme, we carry out perturbative calculations in a formally small parameter $\varepsilon$, where $\varepsilon=4-d$ is a deviation from the upper critical dimension $d_c=4$. We use a nontrivial combination of analytical and numerical tools in order to determine ultraviolet divergent parts of Feynman diagrams.

cond-mat.stat-mech↗

arXiv2017

Software-defined subcarrier wave quantum networking operated by OpenFlow protocol

Future practical implementation of secure quantum communication technology in a multiuser network environment would require automatic monitoring of the optical link condition and quantum system parameters, along with adjusting them in real time according to protocol restrictions. We demonstrate how software-defined networking (SDN) paradigm can be used for addressing this problem on the example of a subcarrier wave quantum communication system, which is promising for network applications. We propose a novel approach to dynamic quantum network routing and communication security based on SDN OpenFlow protocol. SDN-operated dynamic switching between different data encryption methods, quantum or classic, will enable to organize virtual encoding channels with an ability to set the required Quality of Service level for security/bandwidth. These developments will further increase the feasibility of quantum technologies from the network perspective and contribute to bringing them to industrial scale.

quant-ph↗

arXiv2017

Minimally subtracted six loop renormalization of $O(n)$-symmetric $ϕ^4$ theory and critical exponents

We present the perturbative renormalization group functions of $O(n)$-symmetric $ϕ^4$ theory in $4-2\varepsilon$ dimensions to the sixth loop order in the minimal subtraction scheme. In addition, we estimate diagrams without subdivergences up to 11 loops and compare these results with the asymptotic behaviour of the beta function. Furthermore, we perform a resummation to obtain estimates for critical exponents in three and two dimensions.

hep-th↗