Finite-Size Scaling and Universality of the Thermal Resistivity of Liquid ${}^4$He near $T_{\lambda }$

Abstract

We present measurements of the thermal resistivity $\rho (t,P,L)$ near the superfluid transition of ${}^4$He at saturated vapor pressure and confined in cylindrical geometries with radii $L=0.5$ and 1.0 $\mu$m ($t\equiv T/T_{\lambda }(P)-1$). For $L=1.0\mu$m measurements at six pressures $P$ are presented. At and above $T_{\lambda }$ the data are consistent with a universal scaling function $F=(L/{\xi }_0{)}^{x/\nu }(R/R_0)$, $X=(L/{\xi }_0{)}^{1/\nu }t$ valid for all $P$ ($R_0$ and $x$ are the pressure-dependent amplitude and effective exponent of the bulk resistivity $R$ and $\xi ={\xi }_0{t}^{-\nu }$ is the correlation length).