Dynamic critical exponent of the Yang--Lee edge singularity at three loops

Abstract

We compute the dynamic critical exponent $z$ of the Yang--Lee edge singularity in relaxational dynamics using perturbative renormalization-group methods to the three-loop order. The calculation combines diagram reduction, analytic two-loop evaluation via parametric integration with hyperlogarithms, and numerical evaluation of three-loop integrals using the Sector Decomposition method. The perturbative series obtained is resummed using Padé and Padé-Borel-Leroy methods to produce estimates of $z$ in various spatial dimensions. The resulting values are consistent with previous perturbative and functional renormalization-group calculations.