Scalar susceptibility of a diluted classical XY model

We analyze the amplitude fluctuations in a diluted 3D classical XY model near the magnetic phase transition, motivated by the unusual localization properties of the amplitude (Higgs) mode recently found at the disordered superfluid-Mott glass quantum phase transition. We calculate the amplitude correlation function and the corresponding scalar susceptibility by means of Monte Carlo simulations. In contrast to the quantum case, in which the scalar susceptibility was found to violate naive scaling, we find that the scalar susceptibility of the classical system fulfills naive scaling (employing the clean critical exponents, as expected from the Harris criterion) as the temperature is varied across the phase transition for several dilutions. We discuss possible reasons for this discrepancy as well as the generality of our findings.