Critical behavior and scaling of confined ³He-⁴He mixtures

When helium is confined to a uniform small dimension L, its behavior is modified due to the limitation of the growth of the correlation length. This has been explored for planar confinement over a wide range of L. Less is known about confined mixtures, especially in the case of the specific heat. Here two principal effects come into play: the magnitude of the correlation length ξ increases, and the measured heat capacity C_px must be converted to C_pΦ, where Φ = μ₃ - μ₄, before finite-size scaling predictions can be verified. The increase in ξ makes a given confinement L "look smaller" as the concentration x is increased. This, as well as changes of L itself, can be used to test predictions of correlation-length scaling. We report measurements of the specific heat of confined mixtures and compare with the well established scaling for the pure system.