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

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.