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

TL;DR

This paper presents the first analytical four-loop calculation of the dynamic critical exponent z in model A of critical dynamics using parametric integration with hyperlogarithms, advancing perturbative methods in critical phenomena.

Contribution

It introduces a novel application of parametric integration with hyperlogarithms to four-loop calculations in critical dynamics, a first in the field.

Findings

First four-loop analytical calculation of exponent z in model A

Application of hyperlogarithm-based parametric integration to critical dynamics

Identification of linear-irreducible diagrams at four loops

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).