Minimal renormalization without ϵ-expansion: Amplitude functions for O(n) symmetric systems in three dimensions below Tc

摘要: Massive field theory at fixed dimension d < 4 is combined with the minimal subtraction scheme to calculate amplitude functions of thermodynamic quantities for O(n) symmetric Φ4 model below Tc in two-loop order. Goldstone singularities arising an intermediate stage calculation are shown cancel among themselves leaving a finite result limit zero external field. From free energy we order parameter, specific heat and helicity modulus (superfluid density) three dimensions. We also q2 part inverse wavenumber-dependent transverse susceptibility χT(q) which provides independent check our modulus. The contributions superfluid density turn out be comparable magnitude one-loop contributions, indicating necessity higher-order calculations Pade-Borel type resummations.