Additive renormalization of the specific heat of O(n) symmetric systems in three-loop order

TL;DR

This paper derives three-loop formulas for the additive renormalization constant and amplitude function of the specific heat in O(n) symmetric systems, providing more precise theoretical predictions relevant for experimental comparisons.

Contribution

It introduces three-loop calculations for the additive renormalization and amplitude functions in the O(n) phi^4 model, improving the accuracy of theoretical predictions.

Findings

Three-loop correction to B(u) is about 3% for n=2.

The correction size may impact future experimental accuracy.

Provides refined theoretical formulas for specific heat near criticality.

Abstract

We present three-loop formulas for the additive renormalization constant A(u,epsilon) and associated renormalization group function B(u) for the specific heat of the O(n) symmetric phi^4 model. Using this result, we obtain also the amplitude function above Tc within the minimally renormalied theory at fixed d=3. At the fixed point, the three-loop correction to B(u) turns out to be small (about 3% for n=2). We note that a correction of this size may become important at the level of accuracy expected in future experiments.