Numerical evidence of superuniversality of the two-dimensional and three-dimensional random quantum Potts models

The random q-state quantum Potts model is studied on hypercubic lattices in dimensions 2 and 3 using the numerical implementation of the strong disorder renormalization group introduced by Kovacs and Igloi [Phys. Rev. B 82, 054437 (2010)]. Critical exponents nu, d(f), and psi at the infinite disorder fixed point are estimated by finite-size scaling for several numbers of states q between 2 and 50. When scaling corrections are not taken into account, the estimates of both d(f) and psi systematically increase with q. It is shown, however, that q-dependent scaling corrections are present and that the exponents are compatible within error bars, or close to each other, when these corrections are taken into account. This provides evidence of the existence of a superuniversality of all two- and three-dimensional random Potts models.