Explicit Renormalization Group for D=2 Random Bond Ising Model with Long-Range Correlated Disorder

Rajabpour, M. A.; Sepehrinia, Reza

doi:10.1007/s10955-007-9443-5

Cited by 7 publications

(12 citation statements)

References 15 publications

(26 reference statements)

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“…However, the LR correlated disorder is a relevant perturbation that changes the critical behavior. 59 This latter result is in accordance with our findings. The conductance and the Fano factor at the Dirac cone given by…”

Section: Random Mass Disordersupporting

confidence: 94%

Two-dimensional Dirac fermions in the presence of long-range correlated disorder

2012

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16 two-column pagesInternational audienceWe consider two dimensional Dirac fermions in the presence of three types of disorder: random scalar potential, random gauge potential, and random mass with long-range correlations decaying as a power law. Using various methods such as the self-consistent Born approximation (SCBA), renormalization group (RG), the matrix Green's function formalism, and bosonization, we calculate the density of states and study the full counting statistics of fermionic transport at lower energy. The SCBA and RG show that the random correlated scalar potentials generate an algebraically small energy scale below which the density of states saturates to a constant value. For the correlated random gauge potential, RG and bosonization calculations provide consistent behavior of the density of states, which diverges at zero energy in an integrable way. In the case of correlated random mass disorder, the RG flow has a nontrivial infrared stable fixed point leading to a universal power-law behavior of the density of states and also to universal transport properties. In contrast to the uncorrelated case, the correlated scalar potential and random mass disorders give rise to deviation from the pseudodiffusive transport already to lowest order in disorder strength

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Section: Random Mass Disordersupporting

confidence: 94%

Two-dimensional Dirac fermions in the presence of long-range correlated disorder

2012

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“…Interestingly, disorder is a marginally irrelevant perturbation at the new long-range random fixed point, which means that ν = 2/a. This relation was proved to be exact at all orders in perturbation [15] and was later confirmed by Monte Carlo simulations of the 3D Ising model [16] and an explicit RG calculation of the 2D Ising model [17].…”

Section: Introductionmentioning

confidence: 71%

“…It is tempting to associate the boundaries of this intermediate regime to the two temperature scales introduced by the two Potts couplings J 1 and J 2 . In the case presented here, these two couplings are solutions of the self-duality condition (17) with r = J 2 /J 1 = 3. Numerically, J 1 ≃ 0.4812 and J 2 ≃ 1.4436.…”

Section: A Ising Modelmentioning

confidence: 89%

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

Chatelain

2014

Phys. Rev. E

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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. 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.

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“…Thus the anomalous dimension calculated in Ref. [52] from the scaling of the two-point fermionic correlation function can not be directly connected with the critical exponent η. Nevertheless using the Dirac representation allows one to derive a compact formula for the square of the correlation function [34] G(r…”

Section: Spin-spin Correlation At Criticality: Bosonizationmentioning

confidence: 94%

“…This has been done to one-loop order in Refs. [20,52]. We extend these calculations to two-loop order and also compute the averaged square of the spin-spin correlation function to the lowest order using bosonization.…”

Section: Introductionmentioning

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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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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Explicit Renormalization Group for D=2 Random Bond Ising Model with Long-Range Correlated Disorder

Cited by 7 publications

References 15 publications

Two-dimensional Dirac fermions in the presence of long-range correlated disorder

Two-dimensional Dirac fermions in the presence of long-range correlated disorder

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

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

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