Universality of the Kosterlitz-Thouless Transition inHe4Films as a Function of Thickness

We report new measurements of thermal transport in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films near the superfluid transition. We have done this to check on the universality of this transition as a function of thickness or $T_c$ between 1.37 and 1.88 K. Results from this study show for the first time a thickness or $T_c$ dependence of the two characteristic parameters for the thermal conduction, the ratio of diffusion constant to vortex core radius, $\frac{D}{a^2}$, and the nonuniversal constant $b$. We suggest that the increase of $b$ with film thickness is related to the bulk correlation length.