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

TL;DR

This study uses Monte Carlo simulations and finite size scaling to analyze the superfluid transition of helium-4 in aerogel, providing new insights into critical exponents and hyperscaling relations.

Contribution

It introduces a simulation-based analysis of helium-4 in aerogel, challenging previous experimental interpretations of the heat capacity exponent and hyperscaling.

Findings

Correlation length exponent ν=0.73±0.02

Supports hyperscaling with α≈-0.2

Reinterprets previous experimental results

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.