Higgs mode in a diluted classical magnet

Recent results[1] have shown that the Higgs(amplitude) mode at a disordered quantum phase transition features unusual localization properties. Here, we analyze the Higgs mode in a diluted 3D classical xy-model near the magnetic phase transition. To this end, we calculate the amplitude correlation function and the corresponding scalar susceptibility by means of Monte Carlo simulations. We determine if the Higgs mode is localized, like in the quantum case, or remains extended when the temperature is varied across the critical point. We also test whether the scalar susceptibility fulfills naive scaling(in contrast to the quantum case).

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