Finite-size scaling and the convective conductance and specific heat of planar helium films near the superfluid transition

We have measured the convective conductance of saturated helium films at the superfluid transition. Our data show that the Kosterlitz-Thouless features of the transition established for thinner films are retained for all the films we have measured up to 156 A. The finite-size scaling hypothesis is examined, and it is found that the shift in transition temperature is governed by an exponent less than that of the three-dimensional correlation length. This result agrees with earlier results of the specific heat of films. A comparison of the conductance and specific-heat data shows that for films of equal thickness the divergence in the conductance is well below the temperature of the specific-heat maximum. While this is expected for the superfluid transition in two dimensions, we point out, however, that the specific-heat maximum for the thick films is not due to two-dimensional effects. We find that at both of these temperatures the three-dimensional phase correlation length would be substantially less than the thickness of the film.