Critical Scaling Properties at the Superfluid Transition of $^4$He in Aerogel

Details Critical Scaling Properties at the Superfluid Transition of $^4$He in Aerogel Critical Scaling Properties at the Superfluid Transition of $^4$He in Aerogel

2006-03-30

arxiv.org/abs/cond-mat/0603825v2

Phys. Rev. Lett. 97, 225702 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.97.225702

We study the superfluid transition of $^4$He in aerogel by Monte Carlo simulations and finite size scaling analysis. Aerogel is a highly porous silica glass, which we model by a diffusion limited cluster aggregation model. The superfluid is modeled by a three dimensional XY model, with excluded bonds to sites on the aerogel cluster. We obtain the correlation length exponent $\nu=0.73 \pm 0.02$, in reasonable agreement with experiments and with previous simulations. For the heat capacity exponent $\alpha$, both experiments and previous simulations suggest deviations from the Josephson hyperscaling relation $\alpha=2-d\nu$. In contrast, our Monte Carlo results support hyperscaling with $\alpha= -0.2\pm 0.05$. We suggest a reinterpretation of previous experiments, which avoids scaling violations and is consistent with our simulation results.

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