Multiloop calculations with parametric integration in critical dynamics: the four-loop analytic study of model A of $\phi^4$ theory

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

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arXiv · 2512.10591

Multiloop calculations with parametric integration in critical dynamics: the four-loop analytic study of model A of $\phi^4$ theory

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

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Abstract

We perform an analytical four loop calculation of exponent $z$ in model A of critical dynamics in $d=4-2\varepsilon$ dimensions. This is the first time such a large order of perturbation theory has been calculated analytically for models of critical dynamics. To do this, we apply the modern method of parametrical integration with hyperlogaritms. We discuss in detail peculiarities of application of this method to critical dynamics, e.g. the problem of linear-irreducible diagrams already present in four loop (contrary to statics where the first linear-irreducible diagram appears in six loop).

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BibTeX RIS

Loran Ts. Adzhemyan, Diana A. Davletbaeva, Daniil A. Evdokimov, Mikhail V. Kompaniets. 2025-12-11. Multiloop calculations with parametric integration in critical dynamics: the four-loop analytic study of model A of $\phi^4$ theory. https://arxiv.org/abs/2512.10591

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