Magnetic skyrmions at the scale of tens of nanometers are actively discussed in the last decade. These topological objects are experimentally observed as skyrmion crystals (SkX) in a tightly packed triangular configuration. The main focus of experimental investigations and numerical modeling nowadays shifts to the preparation and manipulation of individual skyrmions, aiming to use them ...
Magnetic skyrmions are topologically nontrivial whirls of local magnetization, that can arrange into regular lattices, co-called skyrmion crystals (SkX). Dzyaloshinskii-Moriya interaction (DMI) is one of SkX stabilization mechanisms. There is a wide region on a phase diagram of a thin ferromagnetic film with DMI in a presence of an external magnetic field where SkX is a ground state of the...
We explore superfluidity in $SU(N)$ Fermi gases using the functional renormalization group. Going beyond mean-field we track the flow of the effective action and resolve thermodynamics near the transition. Our study uncovers a fluctuation-induced first-order superfluid transition for $N \geq 4$, absent at mean-field level. We quantify the critical temperature and the discontinuities in the...
In this work, we employ a field-theoretic renormalization group approach to study a paradigmatic model of directed percolation. We focus on the perturbative calculation of the equation of state, extending the analysis to the three-loop order in the expansion parameter $\varepsilon = 4-d$. The main aims of this study are to provide an update on this ongoing work and to present the numerical...
We consider the $f f \rightarrow f f$ scattering amplitudes for the a massless four-fermion interaction model in four dimensions. At first we take the simplest version with the scalar current-current interaction. The loop corrections up to the three-loop level are calculated within the spinor-helicity formalism using the Weyl spinors. We find out that there are two independent spinor...
The talk is devoted to the three-loop renormalization of the effective action for a two-dimensional pricipal chiral field model using the background field method and a cutoff regularization in the coordinate representation. The coefficients of the renormalization constant and the necessary auxiliary vertices are found. Asymptotic expansions for all three-loop diagrams and their dependence on...
We study a stochastic version of magnetohydrodynamics (MHD) formulated as the generalized A-model of a passively advected vector field with full back-reaction on the flow. The model includes parity breaking via a helicity parameter ρ and a continuous interaction parameter A that interpolates between important physical limits (A = 1 for MHD, A = 0 for passive vector advection). Using the...
We performed a two-loop field-theoretic analysis of incompressible, helical magnetohydrodynamics (MHD) in a fully developed, statistically stationary turbulent state. A distinctive feature of turbulence in helical media is the emergence, within the loop expansion of the magnetic response function, of an infrared-relevant, mass-like contribution. Physically, this term corresponds to a...
The study of critical dynamics in the vicinity of the superfluid phase transition presents an unresolved problem: determining the power-law behavior of viscosity upon approaching the critical point. The corresponding dynamic critical exponent remains unknown. Within a phenomenological model, direct computations prove exceedingly complex; the renormalization procedure involves the mixing of...
Hwa–Kardar "running' sandpile model was an attempt to construct a continuous stochastic equation (an effective coarse-grained large-scale description), the derivation of which is based solely on conservation laws, relevant symmetries and dimensionality considerations, in order to capture the hypothetical mechanism behind self-organized criticality, namely, transport in a driven diffusive...
Employing the renormalization group method, we study the behavior of the explicitly anisotropic Hwa-Kardar sandpile model encompassed by an explicitly isotropic randomly moving medium. The motion of the medium is described by the stochastic Navier-Stokes equation with a random stirring force of a rather general form that includes, in particular, the overall shaking of the system and a...
The talk is devoted to the model of random walk on a fluctuating rough surface using the field-theoretic renormalization group (RG). The surface is modelled by the well-known Kardar-Parisi-Zhang (KPZ) stochastic equation while the random walk is described by the standard diffusion equation for a particle in a uniform gravitational field. In the RG approach, possible types of infrared (IR)...
Tricritical behavior in systems with an $n$-component order parameter $\varphi = \{\varphi_k, k = 1, \ldots, n\}$ is described by the action
\begin{equation}
S(\varphi) = \frac{1}{2}\partial_i\varphi_k\partial_i\varphi_k + \frac{\tau_0}{2} \varphi_k\varphi_k + \frac{\lambda_0}{4!} (\varphi_k\varphi_k)^2 + \frac{g_0}{6!} (\varphi_k\varphi_k)^3,
\end{equation}
where the coefficients...
In this talk, using the calculation of the dynamic critical exponent $z$ in the Model A in the four-loop approximation as an example, we will present the diagram reduction technique. This method allows for a substantial decrease in both the number of diagrams and divergent dynamic subgraphs, thereby facilitating subsequent parametric integration with Goncharov polylogarithms.
This talk presents the application of parametric integration with Goncharov polylogarithms to multiloop analytic calculations in models of critical dynamics. The technique has been successfully applied in various high-energy physics and static critical models. Its main requirement is linear reducibility of the integrals under evaluation. In dynamical models, linearly non-reducible integrals...
The renormalization-group approach is used to investigate the possible IR behavior of a randomly walking particle in a random dynamic environment. The particle movement is modeled by the stochastic Fokker -- Planck equation. The dynamics of the environment are described by a random drift field $F_j$ with a pair correlator, which implies two limiting cases -- a "rapidly-changing" and...
The field-theoretic renormalization group (RG) method was used to study the behavior of a randomly walking particle on a rough surface. The surface was given by the conserved Kardar--Parisi--Zhang (CKPZ) stochastic equation, and the random walk was governed by the standard diffusion equation for a particle in a uniform gravitational field. The complete model was presented as a field-theoretic...
