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Journal of Magnetism and Magnetic Materials

Numerical simulation of nonequilibrium critical behavior of the weakly disordered three-spin-state Potts model

В. Н. Бородихин

Published May 24, 2025• 0 citations
Publisher
DOI
10.1016/j.jmmm.2025.173174

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Physical review. E•Jul 24, 2023•3 citations
The results of computer simulations of the critical behavior of three-dimensional structures described by disordered Potts models with q = 3 and q = 4 spin states are discussed. Systems with linear dimensions L = 20–60 with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 are examined. It is found that in a three-dimensional Potts model with q = 3 spin states, introducing nonmagnetic impurities induces a second order phase transition. In a Potts model with q = 4, on the other hand, a shift from a first order phase transition to a second order phase transition is observed at high dilution (p = 0.65). Numerical values of the critical parameters are found using finite-size scaling theory and it is shown that they form a universality class corresponding to disordered systems.
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.