  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.
