Numerical evidences of a universal critical behavior of 2D and 3D random quantum clock and Potts models

TL;DR

This study investigates the critical behavior of 2D and 3D random quantum clock and Potts models, providing numerical evidence that both models share the same infinite-disorder fixed point despite different phase behaviors.

Contribution

It offers the first numerical evidence that the critical behavior of 2D and 3D random quantum clock and Potts models is governed by the same infinite-disorder fixed point, regardless of the number of states.

Findings

No Griffiths phase in 2D clock model.

Evidence of Griffiths phases in the 2D Potts model.

Critical behavior governed by the same fixed point for both models.

Abstract

The random quantum $q$-state clock and Potts models are studied in 2 and 3 dimensions. The existence of Griffiths phases is tested in the 2D case with $q=6$ by sampling the integrated probability distribution of local susceptibilities of the equivalent McCoy-Wu 3D classical modelswith Monte Carlo simulations. No Griffiths phase is found for the clock model. In contrast, numerical evidences of the existence of Griffiths phases in the random Potts model are given and the Finite Size effects are analyzed. The critical point of the random quantum clock model is then studied by Strong-Disorder Renormalization Group. Despite a chaotic behavior of the Renormalization-Group flow at weak disorder, evidences are given that this critical behavior is governed by the same Infinite-Disorder Fixed Point as the Potts model, independently from the number of states $q$.