Critical Behaviour of Superfluid $^4$He in Aerogel

Details Critical Behaviour of Superfluid $^4$He in Aerogel Critical Behaviour of Superfluid $^4$He in Aerogel

1995-02-28

arxiv.org/abs/cond-mat/9502120v1

Physics

Condensed Matter

4 pages, RevTex, 3 postscript figures, LaTeX file and figures have been uuencoded.

Scientific paper

10.1103/PhysRevLett.75.1328

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 $\alpha$ 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 $\zeta$ 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 $\zeta$ from $0.67 \pm 0.005 $ for the pure case to an apparent value of $0.722\pm 0.005$ in the presence of the fractal disorder, provided that the helium correlation length does not exceed the fractal correlation length.

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