High-precision determination of the critical exponents for the lambda-transition of 4He by improved high-temperature expansion

TL;DR

This paper precisely determines critical exponents for the lambda-transition in liquid helium using improved high-temperature series analysis, aligning well with experimental data and reducing previous uncertainties.

Contribution

It provides the most accurate theoretical estimates of critical exponents for the 4He lambda-transition by eliminating leading corrections to scaling in high-temperature expansions.

Findings

Critical exponent ν = 0.67166(55)

Critical exponent γ = 1.3179(11)

Critical exponent α = -0.0150(17)

Abstract

We determine the critical exponents for the XY universality class in three dimensions, which is expected to describe the $\lambda$-transition in ${}^4$He. They are obtained from the analysis of high-temperature series computed for a two-component $\lambda\phi^4$ model. The parameter $\lambda$ is fixed such that the leading corrections to scaling vanish. We obtain $\nu = 0.67166(55)$, $\gamma = 1.3179(11)$, $\alpha=-0.0150(17)$. These estimates improve previous theoretical determinations and agree with the more precise experimental results for liquid Helium.