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

Abstract

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.

arXiv comment4 pages, 3 figures

References in corpus (5)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Critical behavior of the three-dimensional XY universality class
• The specific heat of superfluids near the transition temperature
• Critical Behaviour of Superfluid ${}^4$He in Aerogel
• New universality class for the three-dimensional XY model with correlated impurities: Application to ${}^4$He in aerogels

Cited by in corpus (1)

• Equilibrium phases of two-dimensional bosons in quasi-periodic lattices