Testing The Universality Of The Lambda Transition Using Conned Helium Mixtures

Abstract. 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 connement, 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. Conned 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 connement. However, universality predicts the value of the critical exponent that describes the behavior near the transition should not be affected. Therefore, mixtures conned to a planar lm should scale with the same critical exponent as pure 4He, regardless of concentration or magnitude of lm thickness. We used two different planar connement cells: one at 48.3 nm and a second at 986.9 nm. We compare specic heat data taken from seven different concentrations split between the two cells and use nite-size scaling theory in an attempt to collapse all the data onto a universal curve using a single critical exponent