arXiv subjects

D. A. Evdokimov

Publications and source records attributed to D. A. Evdokimov.

3 recordsLinked to original sources

arXiv2026

Evidence for an Obstruction to Perturbative Renormalization Group in Stochastic Turbulence

We examine whether the perturbative renormalization group (RG) regime of stochastic turbulence can be continued from small $\varepsilon$ to the physical value $\varepsilon_{\mathrm{phys}}=2$, corresponding to large-scale forcing. Exploiting the simplifications of the large-$d$ limit, we calculate the correction exponent $ω$ to five-loop order and find a simple structure suggesting a closed analytic form. This form implies that the fixed point stable near $\varepsilon=0$ ceases to be simultaneously real and infrared stable before reaching $\varepsilon_{\mathrm{phys}}=2$, pointing to a possible change of infrared regime rather than a controlled perturbative RG extrapolation.

nlin.CD↗

arXiv2022

Model A of critical dynamics: 5-loop $\varepsilon$ expansion study

We have calculated the five-loop RG expansions of the $n$-component A model of critical dynamics in dimensions $d=4-\varepsilon$ within the Minimal Subtraction scheme. This is made possible by using the advanced diagram reduction method and the Sector Decomposition technique adapted to the problems of critical dynamics. The $\varepsilon$ expansions for the critical dynamic exponent $z$ for an arbitrary value of the order parameter dimension $n$ are derived. Based on these series, the numerical estimates of $z$ for different universality classes are extracted and compared with the results obtained within different theoretical and experimental methods.

cond-mat.stat-mech↗

arXiv2021

The dynamic critical exponent $z$ for 2d and 3d Ising models from five-loop $ε$ expansion

We calculate the dynamic critical exponent $z$ for 2d and 3d Ising universality classes by means of minimally subtracted five-loop $\varepsilon$ expansion obtained for the one-component model A. This breakthrough turns out to be possible through the successful adaptation of the Sector Decomposition technique to the problems of critical dynamics. The obtained fifth perturbative order accompanied by the use of advanced resummation techniques for asymptotic series allows us to find highly accurate numerical estimates of $z$: for two- and three-dimensional cases we obtain $\boldsymbol{2.14(2)}$ and $\boldsymbol{2.0235(8)}$ respectively. The numbers found are in good agreement with recent results obtained using different approaches.

cond-mat.stat-mech↗