Revised version of "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 five-loop analytic calculation of the specific heat's additive renormalization in the  theory, providing precise amplitude ratios for three-dimensional systems that align with experimental data.

Contribution

It introduces a five-loop calculation method for the specific heat in  theory without new integrations, enhancing accuracy of universal amplitude ratios in three dimensions.

Findings

Calculated Borel resummed amplitude ratios A+/A- for n=1,2,3.

Confirmed smallness of higher-order contributions in resummations.

Achieved high-precision agreement with experimental results for n=2.

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 function F+(u) of the specific heat in three dimensions for n=1,2,3 above T_c and F-(u) for n=1 below T_c up to five-loop order, without using the \epsilon=4-d expansion. 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. Combining our results for B(u) and F+(u) for n=1,2,3 with those of a recent three-loop calculation of F-(u) for general n in d=3 dimensions we calculate Borel resummed universal amplitude ratios A+/A- for n=1,2,3. Our result for A+/A- = 1.056 +/- 0.004 for n=2 is significantly more accurate than the previous result obtained from the \epsilon expansion up to O(\epsilon^2) and agrees well with the high-precision experimental result A+/A- = 1.054 +/- 0.001 for He(4) near the superfluid transition obtained from a recent experiment in space.