Minimal renormalization without epsilon-expansion: Amplitude functions in three dimensions below T_c

TL;DR

This paper employs massive field theory and minimal subtraction at fixed dimension to accurately compute amplitude functions of thermodynamic quantities in the three-dimensional O(n) model below T_c, addressing Goldstone singularities and providing detailed results for superfluid density and specific heat.

Contribution

It introduces a two-loop calculation method for amplitude functions in three dimensions without epsilon-expansion, handling Goldstone singularities and validating results through susceptibility analysis.

Findings

Goldstone singularities cancel out, yielding finite results.

Two-loop contributions are comparable to one-loop, highlighting the need for higher-order calculations.

Calculated amplitude functions for order parameter, specific heat, and superfluid density below T_c.

Abstract

Massive field theory at fixed dimension d<4 is combined with the minimal subtraction scheme to calculate the amplitude functions of thermodynamic quantities for the O(n) symmetric phi^4 model below T_c in two-loop order. Goldstone singularities arising at an intermediate stage in the calculation of O(n) symmetric quantities are shown to cancel among themselves leaving a finite result in the limit of zero external field. From the free energy we calculate the amplitude functions in zero field for the order parameter, specific heat and helicity modulus (superfluid density) in three dimensions. We also calculate the q^2 part of the inverse of the wavenumber-dependent transverse susceptibility chi_T(q) which provides an independent check of our result for the helicity 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 calculations and Pade-Borel type resummations.