Renormalization-Group Theory and Universality along the Lambda Line of $^4$He

TL;DR

This paper reviews the renormalization-group predictions for superfluid density and specific heat near the lambda transition of helium-4, emphasizing universal amplitude ratios and proposing higher-order calculations to test RG universality.

Contribution

It introduces a new theoretical project involving higher-order calculations of amplitude functions to rigorously test RG universality predictions for helium-4.

Findings

Review of RG predictions on superfluid density and specific heat

Focus on universal amplitude ratios near the lambda line

Proposal for higher-order calculations of amplitude functions

Abstract

The present status of the renormalization-group (RG) predictions on the superfluid density $\rho_s$ and the specific heat $C^+$ and $C^-$ near the $\lambda$-line of $^4He$ is briefly reviewed. Particular attention is given to universal amplitude ratios related to these quantities. The goals of a new theory project are presented that involves higher-order calculations of the amplitude functions of $\rho_s, C^+$ and $C^-$ which are of fundamental importance for a test of the universality predictions of the RG theory.