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Theory of Turbulence for $d \rightarrow \infty$: Four-Loop Approximation of the Renormalization Group by Adzhemyan, Loran Ts.; Kirienko, Yury is a scholarly article available to read on EtoBox.

What is Theory of Turbulence for $d \rightarrow \infty$: Four-Loop Approximation of the Renormalization Group about?

Within the framework of the renormalization group approach in the stochastic model of fully developed turbulence, the $\beta$-function has been calculated in the fourth order of perturbation theory for high-dimensional spaces $d \rightarrow \infty$. The position of the fixed point of the renormalization group in the fourth order of the $\varepsilon$-expansion has been determined, and the index $\omega$, which defines the infrared stability of this point, has been calculated. We demonstrate the possibility of significantly reducing the number of Feynman diagrams through mutual cancellation. The results obtained allow us to find the four terms of the $\varepsilon$-expansion of the index $\omega$: $$ \omega = 2\,\varepsilon + \frac{2}{3}\,\varepsilon^2 + \frac{10}{9}\,\varepsilon^3 + \frac{56}{27}\,\varepsilon^4. $$

Author

Adzhemyan, Loran Ts.; Kirienko, Yury

Published

2024

Language

EN