Model A of critical dynamics: 5-loop $\varepsilon$ expansion study

TL;DR

This paper presents a five-loop renormalization group analysis of a critical dynamic model, deriving epsilon expansions for the dynamic exponent z and providing numerical estimates for various universality classes, enhancing precision in critical dynamics predictions.

Contribution

It introduces an advanced diagram reduction and sector decomposition method for five-loop calculations in critical dynamics, deriving epsilon expansions for the dynamic exponent z for any n.

Findings

Derived epsilon expansions for the dynamic critical exponent z.

Provided numerical estimates of z for different universality classes.

Compared theoretical estimates with experimental and other theoretical results.

Abstract

We have calculated the five-loop RG expansions of the $n$-component A model of critical dynamics in dimensions $d=4-\varepsilon$ within the Minimal Subtraction scheme. This is made possible by using the advanced diagram reduction method and the Sector Decomposition technique adapted to the problems of critical dynamics. The $\varepsilon$ expansions for the critical dynamic exponent $z$ for an arbitrary value of the order parameter dimension $n$ are derived. Based on these series, the numerical estimates of $z$ for different universality classes are extracted and compared with the results obtained within different theoretical and experimental methods.