Calculation of the dynamical critical exponent in the model A of critical dynamics to order \epsilon^4

TL;DR

This paper introduces a new numerical method based on the R'-operation for calculating renormalization constants, enabling the precise determination of the dynamical critical exponent z in model A at four-loop order.

Contribution

It presents a novel approach using R'-operation to compute renormalization constants and the dynamical critical exponent to order  in -expansion for model A.

Findings

Calculated the renormalization group functions at four-loop order.

Determined the dynamical critical exponent z to order  in -expansion.

Validated the method's effectiveness for critical dynamics calculations.

Abstract

A new method based on the R'-operation of the renormalization theory is proposed for the numerical calculation of the renormalization constants in the theory of critical behaviour. The problem of finding residues of the poles of the Green's functions at \epsilon = 0, where \epsilon = 4 - d, is reduced to the evaluation of multiple UV-finite integrals, which can be performed by means of standard integration programs. The method is used to calculate the renormalization group functions of the model A of critical dynamics in four-loop approximation. Dynamical exponent z of the model A is calculated in the fourth order of the \epsilon-expansion.