Multi-Loop Calculations of Anomalous Exponents in the Models of Critical Dynamics

¹ Department of Theoretical Physics, St. Petersburg State University, Uljanovskaja 1, 198504, St. Petersburg, Petrodvorez, Russia
² Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, 141980, Dubna, Moscow Region, Russia
³ Department of Theoretical Physics, SAS, Institute of Experimental Physics, Watsonova 47, 040 01, Košice, Slovakia
⁴ Faculty of Science, P. J. Šafárik University, Šrobárova 2, 041 54, Košice

^a e-mail: danco@saske.sk
^b e-mail: hnatic@saske.sk

Published online: 9 February 2016

Abstract

The Renormalization group method (RG) is applied to the investigation of the E model of critical dynamics, which describes the transition from the normal to the superfluid phase in He⁴. The technique “Sector decomposition” with R’ operation is used for the calculation of the Feynman diagrams. The RG functions, critical exponents and critical dynamical exponent z, which determines the growth of the relaxation time near the critical point, have been calculated in the two-loop approximation in the framework of ε-expansion. The relevance of a fixed point for helium, where the dynamic scaling is weakly violated, is briefly discussed.