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arXiv · 2610.01507

Evidence for an Obstruction to Perturbative Renormalization Group in Stochastic Turbulence

L. Ts. Adzhemyan·D. A. Davletbaeva·D. A. Evdokimov·M. V. Kompaniets
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Abstract

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.

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L. Ts. Adzhemyan, D. A. Davletbaeva, D. A. Evdokimov, M. V. Kompaniets. 2026-10-01. Evidence for an Obstruction to Perturbative Renormalization Group in Stochastic Turbulence. https://arxiv.org/abs/2610.01507

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