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

Abstract

We have calculated the five-loop RG expansions of the $n$-component A model of critical dynamics in dimensions $d=4-\epsilon$ 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 $\epsilon$ 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.

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