Griffiths phase and critical behavior of the two-dimensional Potts models with long-range correlated disorder

We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as ∼ r −a . Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to twoloop order. We show that beside the Gaussian fixed point the flow equations have a non trivial fixed point which is stable for 0.995 < a < 2 and is characterized by the correlation length exponent ν = 2/a + O ((2 − a) 3 ). Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent η2 = 1/2 − (2 − a)/4 + O ((2 − a) 2 ).

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“…The numerical simulations of Ref. [66] are in favor of the first scenario but this still remains an open question.…”

Section: Discussionmentioning

confidence: 99%

Critical behavior of the two-dimensional Ising model with long-range correlated disorder

Dudka¹,

Fedorenko²,

Blavatska³

et al. 2016

Phys. Rev. B

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“…For 2D Potts models with a similar disorder construction as used here, Chatelain [10,11] obtained interesting hyperscaling violations related to lack of self averaging, and Griffiths phases. While we consider a different model, it is notable that we do not observe these effects in our 3D results.…”

Section: Discussionmentioning

confidence: 73%

“…Potts models in 2D were studied in Refs. [10,11]. Here we study the different case of a random bond Ising model in 3D.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional universality class of the Ising model with power-law correlated critical disorder

et al. 2019

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We use large-scale Monte Carlo simulations to test the Weinrib-Halperin criterion that predicts new universality classes in the presence of sufficiently slowly decaying power-law-correlated quenched disorder. While new universality classes are reasonably well established, the predicted exponents are controversial. We propose a method of growing such correlated disorder using the three-dimensional Ising model as benchmark systems both for generating disorder and studying the resulting phase transition. Critical equilibrium configurations of a disorder-free system are used to define the two-value distributed random bonds with a small power-law exponent given by the pure Ising exponent. Finite-size scaling analysis shows a new universality class with a single phase transition, but the critical exponents ν d = 1.13(5), η d = 0.48(3) differ significantly from theoretical predictions. We find that depending on details of the disorder generation, disorder-averaged quantities can develop peaks at two temperatures for finite sizes. Finally, a layer model with the two values of bonds spatially separated to halves of the system genuinely has multiple phase transitions and thermodynamic properties can be flexibly tuned by adjusting the model parameters.

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“…Thus, these models are intermediate between random and quasiperiodic systems: all excitations localize at weak disorder, but the clean critical points need not be unstable. Hyperuniform couplings are a particular type of correlated disorder, for which both localization [37][38][39] and phase transitions [40][41][42][43] have been explored; these previous works, however, were concerned with the case of locally correlated disorder, whereas the present work addresses local anticorrelations, which naturally give rise to entirely different physics.…”

Section: Introductionmentioning

confidence: 99%

Quantum criticality in Ising chains with random hyperuniform couplings

2019

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We study quantum phase transitions in transverse-field Ising spin chains in which the couplings are random but hyperuniform, in the sense that their large-scale fluctuations are suppressed. We construct a one-parameter family of disorder models in which long-wavelength fluctuations are increasingly suppressed as a parameter α is tuned. For α = 0, one recovers the familiar infiniterandomness critical point. For 0 < α < 1, we find a line of infinite-randomness critical points with continuously varying critical exponents; however, the Griffiths phases that flank the critical point at α = 0 are absent at any α > 0. When α > 1, randomness is a dangerously irrelevant perturbation at the clean Ising critical point, leading to a state we call the critical Ising insulator. In this state, thermodynamics and equilibrium correlation functions behave as in the clean system. However, all finite-energy excitations are localized, thermal transport vanishes, and autocorrelation functions remain finite in the long-time limit. We characterize this line of hyperuniform critical points using a combination of perturbation theory, renormalization-group methods, and exact diagonalization. arXiv:1809.04595v1 [cond-mat.stat-mech]

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Griffiths phase and critical behavior of the two-dimensional Potts models with long-range correlated disorder

Cited by 14 publications

References 76 publications

Critical behavior of the two-dimensional Ising model with long-range correlated disorder

Critical behavior of the two-dimensional Ising model with long-range correlated disorder

Three-dimensional universality class of the Ising model with power-law correlated critical disorder

Quantum criticality in Ising chains with random hyperuniform couplings

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