Finite-size-scaling analysis of a simulation of theHe4superfluid transition

Several finite-size scaling techniques are applied to path-integral simulations of the superfluid transition in three-dimensional (3D) ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at low pressure. The twist free energy shows a linear increase with periodic cell length below the transition temperature, which it predicts as 2.19±0.02 K. (The experimental value is 2.172 K.) Fitting the superfluid fraction to the scaled form L${\mathrm{\rho }}_{\mathit{s}}$(t,L)/ρ=Q(${\mathit{L}}^{1/\nu }$t), t=(T-${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{c}}$, gives ${\mathit{T}}_{\mathit{c}}$=2.17±0.05 K and the correlation-length exponent ν=0.72±0.1 (experimentally 0.67). The universal constant (${\mathrm{ħ}}^2$ρ/${\mathit{mkT}}_{\mathit{c}}$)Q(0)=0.50±0.02 found here compares well with the value 0.49±0.01 from recent 3D XY model simulations. Additional analyses that include corrections to scaling are found to yield values for ${\mathit{T}}_{\mathit{c}}$ in agreement with the above estimates. A phenomenological renormalization analysis suggests the superfluid density exponent υ=(1.0–1.3)ν, consistent with the Josephson relation.