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arXiv · 2608.15887

Dynamic critical exponent of the Yang--Lee edge singularity at three loops

Loran Ts. Adzhemyan·Diana A. Davletbaeva·Daniil A. Evdokimov·Mikhail V. Kompaniets
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Abstract

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 Pad\'e and Pad\'e-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.

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Loran Ts. Adzhemyan, Diana A. Davletbaeva, Daniil A. Evdokimov, Mikhail V. Kompaniets. 2026-08-16. Dynamic critical exponent of the Yang--Lee edge singularity at three loops. https://arxiv.org/abs/2608.15887

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