Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorder

Abstract

The $q$-state Potts model with a long-range correlated disorder is studied by means of large-scale Monte Carlo simulations for $q=2,4,8$ and 16. Evidence is given of the existence of a Griffiths phase, where the thermodynamic quantities display an algebraic Finite-Size Scaling, in a finite range of temperatures around the self-dual point. The critical exponents are shown to depend on both the temperature and the exponent of the algebraic decay of disorder correlations, but not on the number of states of the Potts model. The mechanism leading to the violation of hyperscaling relations is observed in the entire Griffiths phase.

18 pages, 16 figures, 12 tables

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• Quantum criticality in Ising chains with random hyperuniform couplings
• Three-dimensional universality class of Ising model with power-law-correlated critical disorder
• Long-range quenched bond disorder in the bi-dimensional Potts model
• Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain
• Critical exponent $\nu$ of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques
• Infinite disorder and correlation fixed point in the Potts model with correlated disorder
• Stability of the Griffiths phase in the 2D Potts model with correlated disorder
• Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach
• Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit