We have performed a high resolution specific heat measurement on 4 He completely filling the pores of Vycor glass. Within 10mK of the superfluid transition we have found a peak in the heat capacity which is only 0.02% the size of the background. The peak can be fit with a rounded version of the "logarithmic singularity" observed in bulk 4 He. Along with the previously observed "2/3" power law dependence of the superfluid density on temperature, this strongly suggests that the disorder imposed by the Vycor is irrelevant to the 3DXY superfluid phase transition. The critical amplitude of the peak, while in agreement with that found in other experiments in dilute superfluid 4 He, is considerably larger than that predicted by the theory of hyperuniversality.One of the foundations of the modern theory of critical phenomena is that all phase transitions are divided into a handful of universality classes, grouped together on the basis of a common symmetry and dimensionality in the ordered phase. Experimentally, one groups phase transitions on the basis of the powerlaws in the reduced temperature t = 1 − T /T C which thermodynamic properties follow very near to the transition temperature T C . The critical exponents of these powerlaws, which can be predicted to high accuracy thanks to the computational machinery of the renormalization group theory (RGT), are the same for all systems within a universality class.Because of its high purity, lack of strain, and the relative ease of precision measurement, the superfluid transition of 4 He is an unrivalled testing ground not only for determining the values of critical exponents but also for answering questions about universality. Very precise measurements of the specific heat of 4 He to within a few nK of T λ , the critical temperature of the superfluid transition, have confirmed the powerlaw The superfluid density has also been measured precisely and under the conditions of saturated vapor pressure is found to obey the powerlawwhere the critical exponent ν = 0.6702 and the critical amplitude ρ S0 = 0.351 g/cm 3 .[3] In both experimental quantities, the agreement between the experimentally determined critical exponents and precise RGT calculations is a stunning confirmation of our understanding of critical phenomena in pure systems.[4] The "logarithmic singularity" in the specific heat of equation 1 and the "2/3 power law" of equation 2 identify the superfluid transition of 4 He as a member of the 3DXY universality class.Another pillar in the theory of critical phenomena is the theory of hyperuniversality.[5] Hyperuniversality is a statement that the amount of energy (measured in units of k B T) per fluctuation is the same for all systems within a universality class. This is expressed by defining thewhere ξ 0 is the critical amplitude of the correlation length. RGT calculations find R = 0.96.[5] While ξ is not accessible directly, it can be calculated from the superfluid density by using the Josephson relation [6] The relation in equation 3 was tested by Ahlers and co-workers,...

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We have examined the vibrational noise originating from 1.3 K pumped helium chambers ͑1 K pots͒ that are continuously filled from the 4.2 K bath through an impedance. The noise can be largely eliminated by either heating the pot or by heating the impedance directly. Noise in 1 K pots has detrimental consequences for the operation of audio frequency torsional oscillators and for high precision thermometry.

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