Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models

Abstract: 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 Igl{\'o}i [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 taking into account. This provides evidence of the existence of a super-universality of all 2D and 3D random Potts models.