The q-state Potts model with 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. 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.The q-state Potts model with 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. 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.

arXiv:1308.0734Physical Review EMar 10, 201421 citations

Phase Diagram and Critical Behaviour of the Two-Dimensional Potts Model with Long-Range Quenched Disorder

Rodolfo Rocha, Leticia F. Cugliandolo, Marco Picco

We study the phase diagram and critical properties of the $q = 3$ and $q = 8$ Potts models with spatially correlated disorder governed by a power-law decay with exponent $a$ . Building on the phase diagram proposed by Chippari et al. [3], where a transition from finite-disorder to infinite-disorder fixed points was identified as a function of a, we refine this picture by using wrapping probabilities of Fortuin-Kasteleyn clusters. Furthermore, using magnetic observables, we clarify the physical origin of the double-peak structure in the magnetic susceptibility and establish the validity of the hyper-scaling relation across all investigated regimes.We study the phase diagram and critical properties of the $q = 3$ and $q = 8$ Potts models with spatially correlated disorder governed by a power-law decay with exponent $a$. Building on the phase diagram proposed by Chippari et al. [3], where a transition from finite-disorder to infinite-disorder fixed points was identified as a function of a, we refine this picture by using wrapping probabilities of Fortuin-Kasteleyn clusters. Furthermore, using magnetic observables, we clarify the physical origin of the double-peak structure in the magnetic susceptibility and establish the validity of the hyper-scaling relation across all investigated regimes.

arXiv:2608.29710Aug 30, 20260 citations

Boundary critical phenomena in the three-state Potts model

Masaki Oshikawa

Jan 1, 19980 citations

Critical behaviour of the 1D q-state Potts model with long-range interactions

Zvonko Glumac, Katarina Uzelac

The critical behaviour of the one-dimensional q-state Potts model with long-range interactions decaying with distance r as r −(1+σ) has been studied in the wide range of parameters 0 < σ ≤ 1 and 1 16 ≤ q ≤ 64. A transfer matrix has been constructed for a truncated range of interactions for integer and continuous q, and finite range scaling has been applied. Results for the phase diagram and the correlation length critical exponent are presented. Short title: Critical behaviour of the 1D LR q-state Potts model Recently, finite range scaling (FRS) appeared as an efficient method to deal with various discrete one-dimensional models with long range (LR) interactions (Glumac and Uzelac, 1989, 1991). The aim of the present study is to apply it to the onedimensional q-state Potts model with LR interactions, defined by the hamiltonianThe critical behaviour of the one-dimensional q-state Potts model with long-range interactions decaying with distance r as r −(1+σ) has been studied in the wide range of parameters 0 < σ ≤ 1 and 1 16 ≤ q ≤ 64. A transfer matrix has been constructed for a truncated range of interactions for integer and continuous q, and finite range scaling has been applied. Results for the phase diagram and the correlation length critical exponent are presented. Short title: Critical behaviour of the 1D LR q-state Potts model Recently, finite range scaling (FRS) appeared as an efficient method to deal with various discrete one-dimensional models with long range (LR) interactions (Glumac and Uzelac, 1989, 1991). The aim of the present study is to apply it to the onedimensional q-state Potts model with LR interactions, defined by the hamiltonian

Jan 1, 199321 citations

Thermodynamics and Low-Temperature Spectrum of the Three-State Potts Model

Rinat Kedem

Jan 1, 19930 citations

We study the phase diagram and critical properties of the

q = 3

and

q = 8

Potts models with spatially correlated disorder governed by a power-law decay with exponent

a

. Building on the phase diagram proposed by Chippari et al. [3], where a transition from finite-disorder to infinite-disorder fixed points was identified as a function of a, we refine this picture by using wrapping probabilities of Fortuin-Kasteleyn clusters. Furthermore, using magnetic observables, we clarify the physical origin of the double-peak structure in the magnetic susceptibility and establish the validity of the hyper-scaling relation across all investigated regimes.