Scalar susceptibility of a diluted classical XY model

The Higgs (amplitude) mode at the disordered superfluid-Mott glass quantum phase transition was recently shown to feature unusual localization properties that violate naive scaling [1,2,3]. To test whether analogous behavior also occurs in the classical case, we analyze the Higgs mode in a diluted 3D classical XY-model near the magnetic 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, we find that the scalar susceptibility 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.

[1] M. Puschmann, J. Crewse, J. A. Hoyos, and T. Vojta, Phys. Rev. Lett. 125, 027002 (2020).

[2] J. Crewse and T. Vojta, Phys. Rev. B 104, 014511 (2021).

[3] M. Puschmann, J.C. Getelina, J.A. Hoyos, and T. Vojta, Ann. Phys. in press , arXiv:2101.11065