Critical Exponents of Superfluid Helium and Pseudo-$\epsilon$ Expansion

Understand

Pseudo-$\epsilon$ expansions ($\tau$-series) for critical exponents of 3D XY model describing $\lambda$-transition in liquid helium are derived up to $\tau^6$ terms.

• Numerical estimates extracted from the $\tau$-series obtained using Pad\'e-Borel resummation technique, scaling relations and seven-loop ($\tau^7$) estimate for the Fisher exponent $\eta$ are presented including those for exponents $\alpha$ and $\nu$ measured in experiments with record accuracy.
• For the exponent $\alpha$ the procedure argued to be most reliable gives $\alpha= -0.0117$.
• This number is very close to the most accurate experimental values differing appreciably from the results of numerous lattice and field-theoretical calculations.