Critical Behaviour of Superfluid $^4$He in Aerogel

TL;DR

This study uses Monte Carlo simulations to investigate how the critical behavior of superfluid helium-4 is affected by the fractal disorder of aerogel, revealing an increase in the superfluid density critical exponent due to the fractal structure.

Contribution

The paper introduces a model of aerogel as a fractal percolating cluster and demonstrates how fractal disorder influences the superfluid critical exponent in helium-4.

Findings

Superfluid density critical exponent increases from 0.67 to approximately 0.722 due to fractal disorder.

Fractal nature of aerogel causes a crossover effect impacting critical behavior.

Monte Carlo simulations support the hypothesis of fractal influence on critical exponents.

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 $\alpha$ 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.