Universal amplitude ratios for the superfluid transition of He-4

We present the results of a three-loop calculation of amplitude functions w ithin the O(n) symmetric phi(4) theory in three dimensions for general it b elow T-c. An appropriate treatment of Goldstone modes avoids spurious singu larities for n > 1. Several universal amplitude ratios are calculated using Borel resummation. Application to n = 2 yields the alpha-insensitive quant ity for the specific heat amplitude ratio P = alpha(-1)(1 - A(+)/A(-)) = 4. 39 +/- 0.26. For the superfluid density we get R-zeta(T) = zeta(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 fo r the superfluid transition of He-4. Accurate knowledge of these amplitude ratios is needed for testing the renormalization-group prediction of critic al-point universality along the lambda-line of superfluid He-4 on earth and under microgravity conditions in space. (C) 2000 Elsevier Science B.V. All rights reserved.