Determination of the bulk helium critical exponents using confined helium

The specific heat of helium homogeneously confined in one or more dimensions is expected to collapse onto a scaling function which depends only on the ratio of the smallest dimension of confinement to the correlation length, written as L/ξ. This may be rewritten to explicitly show the temperature dependence of the correlation length as L/ξ₀t^-ν, where the constant ξ₀ is the prefactor of the correlation length, t is a dimensionless temperature difference from the superfluid transition, and ν is the critical exponent associated with the correlation length. Thus, in principle, one should be able to obtain the exponent ν from the scaling of thermodynamic measurements of confined helium for various L's. This would represent an independent determination of ν distinct from what is obtained using the behavior of the bulk superfluid density, or via the bulk specific heat and the hyperscaling relation. In practice, this analysis is hampered by the lack of a theoretical expression for the scaling function. We present preliminary results of analyses of specific heat data for planar confinement which spans a range of about 1200 in L and yields the exponent ν. The data are fit to an empirical equation which is obtained so that it has the proper asymptotic temperature dependence for large and small values of the scaling variable, which we take as tL^1/ν. Results are compared with theoretical and other experimental determinations of ν.