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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...

The universality of phase transitions is an important prediction of theories of critical behavior. Simply stated, microscopically different systems near a critical point may be described by universal quantities if their dimensionality is the same and the order parameter has the same degrees of freedom. One way to test this idea is to measure the thermodynamic response of a set of systems to an input where the response changes with a variation in some quantity like spatial confinement, impurity concentration, or even pressure. While the response of each system is different, the behavior may still be described by a common critical exponent if the idea of universality is correct. Confined mixtures of 3He‐4He and pure 4He are believed to satisfy these requirements. Here, amplitudes such as the magnitude of the correlation length and the temperature of the transition both depend upon the concentration of the mixture and the extent of confinement. However, universality predicts the value of the critical exponen...

We report on recent measurements of the specific heat of helium confined in pill‐boxes 2 μm across and 2 μm deep made lithographically on a silicon wafer. The experimental cells distribute liquid from a bulk reservoir to ∼ 108 boxes by an array of very shallow fill‐channels (0.019 μm and 0.010 μm) which represent a negligible volume compared to that of the boxes. Since the channels are so shallow, the helium in them becomes superfluid at a much lower temperature than the liquid in the boxes. Therefore, during the course of the heat capacity measurements, the liquid in the channels in always normal, and the cell would be expected to behave as a system of uncoupled boxes. We compare these measurements with one previously made of a cell where the confinement was to 1 μm boxes with an equivalent fill arrangement. While the shift in the position of the specific heat maximum relative to the 1 μm cell is what one would expect on the basis of finite‐size scaling, there are discrepancies in the specific heat amplitude between the 2 μm cell utilizing different depth fill‐channels, and with the 1 μm cell. It is possible that the channels, even though normal and of negligible volume, provide a weak coupling between the boxes leading to a collective rather than single‐box behavior.

We report measurements of the superfluid fraction of 4He confined in small channels 9.4 nm high, 19 μm wide by 2000 μm long. This confinement corresponds to a film of finite lateral extent. The data show a shift in the transition to a lower temperature which is larger than the logarithmic dependence expected from finite‐size scaling and Berezinskǐ ‐Kosterlitz‐Thouless theory. This shift however is smaller than the one proposed by Sobnack and Kusmartsev for this kind of geometry. When examining the behavior of the shift for confinement at several widths, we found that the shift favors a power law with a larger exponent than predicted by Sobnack and Kusmartsev.