Numerical evidence of a universal critical behavior of two-dimensional and three-dimensional random quantum clock and Potts models

The random quantum q-state clock and Potts models are studied in two and three dimensions. The existence of Griffiths phases is tested in the two-dimensional case with q = 6 by sampling the integrated probability distribution of local susceptibilities of the equivalent McCoy-Wu three-dimensional classical models with Monte Carlo simulations. For the random Potts model, numerical evidence of the existence of Griffiths phases is given and the finite-size effects are analyzed. For the clock model, the data also suggest the existence of a Griffiths phase but with much larger finite-size effects. The critical point of the random quantum clock model is then studied with the Strong-Disorder Renormalization Group. Evidence is given that, at strong enough disorder, this critical behavior is governed by the same infinite-disorder fixed point as the Potts model, for all the number of states q considered. At weak disorder, our renormalization group method becomes unstable and does not allow us to make conclusions.

Automated summary

The random quantum q-state clock and Potts models are examined in two and three dimensions. The presence of Griffiths phases is investigated, and numerical evidence supports their existence in both models. The effects of finite-size and disorder strength are analyzed, and evidence suggests a shared critical behavior between the random quantum clock model and the Potts model.