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

TL;DR

This study provides numerical evidence that the critical exponents of 2D and 3D random quantum Potts models are super-universal across different q values, once scaling corrections are properly accounted for.

Contribution

It demonstrates that all 2D and 3D random quantum Potts models share a super-universal set of critical exponents, revealing a unified critical behavior.

Findings

Critical exponents are compatible across q when scaling corrections are included.

Scaling corrections depend on q but do not affect the universality class.

Evidence supports super-universality of 2D and 3D random 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.