Lambda Point in theH4e-Vycor System: A Test of Hyperuniversality

Abstract

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,...

Localized Bose–Einstein Condensation of 4He Confined in Nanoporous Media

“…The peak we observed is rounded and located about 0.2 K below T . These features are commonly observed in a number of confined 4 He systems, such as 4 He in Vycor, [24][25][26]28,29) in slab geometries, 27) and even in 4 He nanodroplets formed in metal. 30) We believe that all of these heat capacity peaks are manifestations of the LBEC states.…”

“…Since the bulk heat capacity shows nearly divergent behavior in the vicinity of the point, we carefully subtracted the bulk contribution from the total heat capacity. The subtraction procedure was adopted from the heat capacity study of 4 He in Vycor by Zassenhaus and Reppy, [24][25][26] and is published elsewhere. 11,23) The heat capacities after the subtractions are shown in Fig.…”

Microscopic theory of a phase transition in a critical region: Bose–Einstein condensation in an interacting gas

“…It is immediate to generalize them to any trapping potentials and boundary conditions. They open a way to solve the long-standing problem of the BEC and other phase transitions [1][2][3][4][5][6][7][8][9][10][11][12], including a restricted canonical ensemble problem [2], and describe numerous modern laboratory and numerical experiments on the critical phenomena in BEC of the mesoscopic systems [22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

“…The problem of the critical region and mesoscopic effects is directly related to numerous modern experiments and numerical studies on the BEC of a trapped gas (including BEC on a chip), where N ∼ 10 2 − 10 7 , (see, for example, [22][23][24][25][26][27][28][29][30][31][32][33]) and superfluidity of 4 He in nanodroplets (N ∼ 10 8 − 10 11 ) [34] and porous glasses [35].…”

Effects of aerogel-like disorder on the critical behavior of O(m)-vector models. Recent simulations and experimental evidence

“…In terms of the WH model, this 4 He-Vycor system falls into the SRC regime (1), so theoretical predictions agree with experiments. Alternatively, Zassenhaus and Reppy [20], reported calorimetric studies for this 4 He-Vycor system, showing that the singular part of specific heat curves fit well a λ-like curve with the same exponent α as bulk SF 4 He. Further experiments, using porous gold to confine SF 4 He, instead of Vycor, confirm these results [21].…”