Universal amplitude ratios for the superfluid transition of He-4

Abstract:
We present the results of a three-loop calculation of amplitude functions within the O(n) symmetric phi^4 theory in three dimensions for general n below Tc. 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 alpha-insensitive quantity for the specific heat amplitude ratio P=alpha^-1(1-A⁺/A^-)=4.39±0.26. For the superfluid density we get R xi^T=xi_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 He-4. Accurate knowledge of these amplitude ratios is needed for testing the renormalization-group prediction of critical-point universality along the -line of superfluid 4He on earth and under microgravity conditions in space.

Keywords:
O(n) symmetry, universal amplitude ratios, superfluid