Unusual behavior of ³He-⁴He mixtures in connected OD boxes

We report on measurements of the specific heat of ³He- ⁴He mixtures confined to boxes connected with fill channels 1 μm wide and 19 nm high. These data were meant as a study of mixtures to test universality of finite-size scaling along the lambda-line. We find instead that the mixtures have very unusual behavior relative to mixtures studied in geometries for 2D and 1D crossover. These latter data can be scaled successfully as long as one does not include data for pure ⁴He. In contrast, the 0D crossover data do not scale on either side of the bulk transition temperature T_λ and have rather different overall behavior: They show a dramatically larger temperature shift of the specific heat maximum C _max relative to data for 2D and ID, the value of the specific heat at T_λ is substantially smaller than that observed for the other dimensionalities, and the value of C_max exceeds the magnitude of the bulk specific heat at the same temperature. This overall behavior is so unusual that it suggests there is a role being played by the connecting channels even though the liquid within them remains in the normal state over the temperature range in which the specific heat is measured.