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

TL;DR

This study investigates how correlated impurities in simulated aerogels affect the critical behavior of the 3D XY model, revealing a new universality class influenced by hidden long-range correlations, supported by Monte Carlo simulations.

Contribution

It introduces a new universality class for the 3D XY model with correlated impurities, supported by simulation data and analysis of critical exponents.

Findings

Critical exponents $ u$ and $eta$ change with impurity concentration.

Evidence of hidden long-range correlations in disorder distributions.

Agreement with experimental observations on $^4$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.