Critical Behavior of Superfluid4He in Aerogel

Abstract

We report on Monte Carlo studies of the critical behaviour of superfluid 4 He in the presence of quenched disorder with long-range fractal correlations. According to the heuristic argument by Harris, uncorrelated disorder is irrelevant when the specific heat critical exponent α is negative, which is the case for the pure 4 He. However, experiments on helium in aerogel have shown that the superfluid density critical exponent ζ changes. We hypothesize that this is a cross-over effect due to the fractal nature of aerogel. Modelling the aerogel as an incipient percolating cluster in 3D and weakening the bonds at the fractal sites, we perform XY-model simulations, which demonstrate an increase in ζ from 0.67 ± 0.005 for the pure case to an apparent value of 0.722 ± 0.005 in the presence of the fractal disorder, provided that the helium correlation length does not exceed the fractal correlation length.PACS numbers: 75.40.Mg, 75.10.Nr, 64.60.Ak It is generally believed that the superfluid transition (λ-point) of pure 4 He belongs to the classical 3D-XY model universality class. Near the critical temperature T c , the superfluid density scales as |T − T c | ζ , where ζ is measured [1] to be 0.674 ± 0.003. There has been considerable interest in studying the superfluid transition for helium in a variety of porous media.[2] One such system is Vycor which is a random glass with a porosity of order 30%. Remarkably, the critical exponent ζ is found to be unchanged by the seemingly huge perturbation represented by the glass. This however is the result expected according to heuristic arguments of Harris [3] and more rigorous recent work [4] which shows that weak, uncorrelated randomness is irrelevant at the unperturbed critical point provided that the specific heat exponent is negative. The exponent [1] α ≈ −0.026±0.004 is indeed negative for 4 He, however Narayan and Fisher [5] have argued that since α is only slightly negative, the crossover to the pure 3D XY critical regime is almost logarithmically slow. Until recently Vycor was the only porous medium in which ζ was observed to be unchanged. New experiments however appear to have added a second material, porous gold (which also has short-range correlations), to the list. [6] Remarkable results have been obtained for the aerogel system. Aerogel is a fractal silica 'dust' with porosities of 95-98% or higher. Despite the fact that aerogel is almost entirely empty space, and that it (unlike Vycor) has only a tiny effect on the critical temperature, the exponent ζ is apparently quite distinctly shifted [7,8,6] to approximately 0.75 (or larger), indicating that the nominally weak aerogel perturbation is relevant at the 3D XY critical point and aerogel (perhaps) produces a new universality class. The specific heat data suggests that either hyperscaling is violated or the amplitude ratio is exceptionally small. [9,10] In addition to shifting ζ and α, aerogel dramatically changes the topology of the 3 He-4 He mixture phase diagram. [11,12] It is known that long-range correlati...

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