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

Abstract

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.