arXiv subjects

Lukáš Mižišin

Publications and source records attributed to Lukáš Mižišin.

6 recordsLinked to original sources

arXiv2026

Magnetohydrodynamics in turbulent dynamo regime: the stability problem

This paper investigates stochastic solenoidal magnetohydrodynamics within the field-theoretic Martin-Siggia-Rose-De Dominicis-Janssen formalism, with a specific focus on the stability of the system when spatial mirror (parity) symmetry is explicitly broken. Under helical forcing, the one-particle-irreducible magnetic response function already at one loop contains a curl-type contribution that dominates the bare resistive term in the infrared limit, leading to exponential instability of the trivial state $\langle \mathbf{b} \rangle = \mathbf{0}$. We re-examine a stabilization mechanism proposed in [L. T. Adzhemyan, et al., Theor. Math. Phys. 72, 940-950 (1987)], in which the system evolves into a phase with a dynamically spontaneously broken rotational symmetry and a generated mean magnetic field $\langle \mathbf{b} \rangle = \mathbf{B}_0$. By deriving a self-consistency condition for $ \mathbf{B}_0$, we show that for any physically admissible (infrared) form of the pumping function, the model admits only a singular solution. We illustrate this with the standard power-law and "massive" pumping functions. We further show that previous claims of a finite $ \mathbf{B}_0$ arose from an inconsistent truncation of asymptotic expansions. We argue that a consistent physical resolution requires including a bare curl term in the stochastic induction equation, which naturally arises from a parity-violating modification of Ohm's law. With this modification, stabilization of the system by spontaneous symmetry breaking becomes a viable field-theoretic description of large-scale mean-field generation (turbulent dynamo) in helical turbulent magnetohydrodynamics.

physics.plasm-ph↗

arXiv2026

Renormalization group analysis of directed percolation process: Towards multiloop calculation of scaling functions

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 $\varepsilon = 4-d$. We show that a large group of the necessary three-loop Feynman diagrams can be mapped onto already existing three-loop results, and develop a technique for the calculation of the remaining -- truly novel -- ones. The described semi-analytic procedure is further used to verify existing two-loop results. The main aim of this study is to provide an update on this ongoing work, as full three-loop calculations utilizing the described procedure are in progress.

cond-mat.stat-mech↗

arXiv2025

Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum

We present a two-loop field-theoretic analysis of incompressible helical magnetohydrodynamics (MHD) in fully developed stationary turbulence. A key feature of helical MHD is the appearance of an infrared-unstable ``mass-like'' term in the loop diagrams of the magnetic response function. Physically, this term corresponds to the relevant perturbation of the Joule damping, proportional to $\boldsymbol{\nabla} \times \boldsymbol{b}$ ($\boldsymbol{b} =$ magnetic field). Its presence destabilizes the trivial ground state $\langle \boldsymbol{b} \rangle = 0$ and forces us to look for a mechanism for stabilizing the system. We show that such stabilization can be achieved in two ways: (i) by introducing into induction equation an external mass-like parameter that precisely cancels these dangerous loop corrections (kinematic regime), or (ii) via spontaneous breaking of the rotational symmetry, leading to a new ground state with nonzero large-scale magnetic field (turbulent dynamo regime). For the latter case, we study the two-loop correction to the spontaneously generated magnetic field and demonstrate that Goldstone-like corrections to Alfvén modes along with some other anisotropic structures arise. Our results also confirm that the emergent mean magnetic field leads to a steeper slope of the magnetic energy spectrum, $-11/3 + 2γ_{b\star}$ (with $γ_{b\star} = -0.1039 - 0.4202ρ^2$, for $|ρ| \leqslant 1$ as the degree of helicity), compared to the Kolmogorov velocity spectrum of $-11/3$, thereby breaking equipartition.

physics.plasm-ph↗

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↗

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↗

arXiv2020

Renormalization group study of superfluid phase transition: effect of compressibility

Dynamic critical behavior in superfluid systems is considered in a presence of external stirring and advecting processes. The latter are generated by means of the Gaussian random velocity ensemble with white-noise character in time variable and self-similar spatial dependence. The main focus of this work is to analyze an effect of compressible modes on the critical behavior. The model is formulated through stochastic Langevin equations, which are then recast into Janssen-De Dominicis response formalism. Employing the field-theoretic perturbative renormalization group method we analyze large-scale properties of the model. Explicit calculations are performed to the leading one-loop approximation in the double $(\varepsilon, y)$ expansion scheme, where $\varepsilon$ is a deviation from the upper critical dimension $d_c = 4$ and $y$ describes a scaling properties of the velocity ensemble. Altogether five distinct universality classes are expected to be macroscopically observable. In contrast to the incompressible case, we found that compressibility leads to an enhancement and stabilization of non-trivial asymptotic regimes.

cond-mat.stat-mech↗