MINIMAL RENORMALIZATION WITHOUT EPSILON-EXPANSION - AMPLITUDE FUNCTIONS FOR O(N) SYMMETRICAL SYSTEMS IN 3 DIMENSIONS BELOW T-C

Massive field theory at fixed dimension d < 4 is combined with the min imal subtraction scheme to calculate the amplitude functions of thermo dynamic quantities for the O(n) symmetric phi(4) model below T-c in tw o-loop order. Goldstone singularities arising at an intermediate stage in the calculation of O(n) symmetric quantities are shown to cancel a mong themselves leaving a finite result in the limit of zero external field, From the free energy we calculate the amplitude functions in ze ro field for the order parameter, specific heat and helicity modulus ( superfluid density) in three dimensions. We also calculate the q(2) pa rt of the inverse of the wavenumber-dependent transverse susceptibilit y chi r(q) which provides an independent check of our result for the h elicity modulus. The two-loop contributions to the superfluid density and specific heat below T-c turn out to be comparable in magnitude to the one-loop contributions, indicating the necessity of higher-order c alculations and Pade-Borel type resummations. (C) 1997 Elsevier Scienc e B.V.