Field theory of bicritical and tetracritical points. IV. Critical dynamics including reversible terms

Abstract: This article concludes a series of papers (R. Folk, Yu. Holovatch, and G. Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)) where the tools of the field theoretical renormalization group were employed to explain and quantitatively describe different types of static and dynamic behavior in the vicinity of multicritical points. Here, we give the complete two loop calculation and analysis of the dynamic renormalization-group flow equations at the multicritical point in anisotropic antiferromagnets in an external magnetic field. We find that the time scales of the order parameters characterizing the parallel and perpendicular ordering with respect to the external field scale in the same way. This holds independent whether the Heisenberg fixed point or the biconical fixed point in statics is the stable one. The non-asymptotic analysis of the dynamic flow equations shows that due to cancelation effects the critical behavior is described - in distances from the critical point accessible to experiments - by the critical behavior qualitatively found in one loop order. Although one may conclude from the effective dynamic exponents (taking almost their one loop values) that weak scaling for the order parameter components is valid, the flow of the time scale ratios is quite different and they do not reach their asymptotic values.