High Precision Measurement of the Thermal Exponent for the Three-Dimensional XY Universality Class

TL;DR

This paper reports a high-precision simulation measurement of the correlation length exponent for the 3D XY universality class, confirming previous results and aligning with experimental data on superfluid helium.

Contribution

The study provides a highly precise numerical estimate of the thermal exponent for the 3D XY universality class, improving accuracy over prior simulations.

Findings

Measured =0.6717(3) for the correlation length exponent

Results agree with recent simulation studies

Results marginally agree with space-based superfluid helium measurements

Abstract

Simulations results are reported for critical point of the two-component $\phi^4$ field theory. The correlation length exponent is measured to high precision with the result $\nu=0.6717(3)$. This value is in agreement with recent simulation results [Campostrini \textit{et al}., Phys. Rev. B \textbf{63}, 214503 (2001)], and marginally agrees with the most recent space-based measurements of the superfluid transition in $^4$He [Lipa \textit{et al}., Phys. Rev. B \textbf{68}, 174518 (2003)].