Finite-Size Scaling and Universality of the Thermal Resistivity of Liquid $^4$He near $T_λ$

Abstract

We present measurements of the thermal resistivity $ρ(t,P,L)$ near the superfluid transition of $^4$He at saturated vapor pressure and confined in cylindrical geometries with radii $L=0.5$ and 1.0 $μ$m ($t\equiv T/T_λ(P) - 1$). For $L = 1.0 μ$m measurements at six pressures $P$ are presented. At and above $T_λ$ the data are consistent with a universal scaling function $F=(L/ξ_0)^{x/ν}(R/R_0)$, $X= (L/ξ_0)^{1/ν}t$ valid for all $P$ ($R_0$ and $x$ are the pressure-dependent amplitude and effective exponent of the bulk resistivity $R$ and $ξ= ξ_0 t^{-ν}$ is the correlation length).