Five-loop additive renormalization in the phi^4 theory and amplitude functions of the minimally renormalized specific heat in three dimensions

TL;DR

This paper performs a detailed five-loop calculation of the additive renormalization and amplitude functions of the specific heat in the O(n) symmetric phi^4 theory, providing precise results for three dimensions and confirming previous conjectures.

Contribution

It introduces a five-loop calculation method for the specific heat's additive renormalization and amplitude functions, extending previous four-loop results without new integrations.

Findings

Accurate five-loop results for specific heat amplitude functions in three dimensions.

Confirmation of the smallness of higher-order contributions through Borel resummation.

Calculation of universal amplitude ratios for n=1,2,3.

Abstract

We present an analytic five-loop calculation for the additive renormalization constant A(u,epsilon) and the associated renormalization-group function B(u) of the specific heat of the O(n) symmetric phi^4 theory within the minimal subtraction scheme. We show that this calculation does not require new five-loop integrations but can be performed on the basis of the previous five-loop calculation of the four-point vertex function combined with an appropriate identification of symmetry factors of vacuum diagrams. We also determine the amplitude functions of the specific heat in three dimensions for n=1,2,3 above T_c and for n=1 below T_c up to five-loop order. Accurate results are obtained from Borel resummations of B(u) for n=1,2,3 and of the amplitude functions for n=1. Previous conjectures regarding the smallness of the resummed higher-order contributions are confirmed. Borel resummed universal amplitude ratios A^+/A^- and a_c^+/a_c^- are calculated for n=1.