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

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Abstract
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 Å. 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.