Universal amplitude ratios for the superfluid transition of 4He

Abstract

We present the results of a three-loop calculation of amplitude functions within the O( n) symmetric φ 4 theory in three dimensions for general n below T c. An appropriate treatment of Goldstone modes avoids spurious singularities for n>1. Several universal amplitude ratios are calculated using Borel resummation. Application to n=2 yields the α-insensitive quantity for the specific heat amplitude ratio P= α −1(1− A +/ A −)=4.39±0.26. For the superfluid density we get R ξ T = ξ 0 T ( A −) 1/3=0.815±0.010. These results are significantly more accurate than previous theoretical estimates and agree well with experimental results for the superfluid transition of 4He. Accurate knowledge of these amplitude ratios is needed for testing the renormalization-group prediction of critical-point universality along the λ-line of superfluid 4He on earth and under microgravity conditions in space.