arXiv subjects

Daniil A. Evdokimov

Publications and source records attributed to Daniil A. Evdokimov.

3 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↗

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↗