New universality class for the three-dimensional XY model with correlated impurities: Application to ${}^4$He in aerogels

Abstract

Encouraged by experiments on ${}^4$He in aerogels, we confine planar spins in the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behavior of the three-dimensional XY model. Monte Carlo simulations and finite-size scaling are used to determine critical couplings $K_c$ and exponents. In agreement with experiments, clear evidence of change in the thermal critical exponents $\nu$ and $\alpha$ is found at nonzero volume fractions of impurities. These changes are explained in terms of {\it hidden} long-range correlations within disorder distributions.

4 pages, 4 figures, submitted to Phys. Rev. Lett

References in corpus (8)

• Critical behavior of the three-dimensional XY universality class
• The Sol-Gel Process Simulated by Cluster-Cluster Aggregation
• The specific heat of superfluids near the transition temperature
• Disorder Averaging and Finite Size Scaling
• Percolation in Cluster-Cluster Aggregation Processes
• Critical Behaviour of Superfluid ${}^4$He in Aerogel
• Theory and Satellite Experiment for Critical Exponent alpha of lambda-Transition in Superfluid Helium
• Invaded cluster simulations of the XY model in two and three dimensions

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• The influence of long-range correlated defects on critical ultrasound propagation in solids
• Three-dimensional Ising model confined in low-porosity aerogels: a Monte Carlo study
• Critical Scaling Properties at the Superfluid Transition of ${}^4$He in Aerogel