Hyperlogarithms in the theory of turbulence of infinite dimension
Abstract
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 highdimensional spaces, which has a propagator that is nonstandard with respect to the HEP: $(i \omega + \nu k^2)^{1}$. 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 $\omega$ responsible for the infrared stability of the fixed point is obtained.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.14533
 arXiv:
 arXiv:2405.14533
 Bibcode:
 2024arXiv240514533A
 Keywords:

 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory
 EPrint:
 16 pages