Random quantum magnets with broad disorder distribution

Karevski, Dragi; Lin, Yueh-hsiang; Rieger, Heiko; Kawashima, Naoki; Iglói, Ferenc

doi:10.1007/pl00011100

Cited by 56 publications

(55 citation statements)

References 23 publications

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“…In dimension d > 1, the strong disorder renormalization procedure can still be defined. It cannot be solved analytically, because the topology of the lattice changes upon renormalization, but it has been studied numerically with the conclusion that the transition is also governed by an Infinite-Disorder fixed point in dimensions d = 2, 3, 4 [4][5][6][7][8][9][10][11][12][13][14]. These numerical renormalization results are in agreement with the results of independent quantum Monte-Carlo in d = 2 [15,16].…”

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confidence: 66%

Random transverse field Ising model in dimensiond> 1: scaling analysis in the disordered phase from the directed polymer model

Monthus¹,

Garel²

2012

J. Phys. A: Math. Theor.

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confidence: 66%

Random transverse field Ising model in dimensiond> 1: scaling analysis in the disordered phase from the directed polymer model

Monthus¹,

Garel²

2012

J. Phys. A: Math. Theor.

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“…[10][11][12] In higher dimensions, in particular, in two dimensions the calculations are numerical and have only limited accuracy. [13][14][15][16][17][18][19] In the present paper we have considered the prototypical model in 2D having an IDFP the random transverse-field Ising model and studied its critical properties by a numerical implementation of the SDRG approach. As follows from the concept of IDFP our numerical results are expected to be asymptotically exact.…”

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confidence: 99%

Renormalization group study of the two-dimensional random transverse-field Ising model

2010

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The infinite-disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to L = 2048. We have calculated sample dependent pseudocritical points and studied their distribution, which is found to be characterized by the same shift and width exponent: = 1.24͑2͒. For different types of disorder the infinite-disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: x = 0.982͑15͒ and = 0.48͑2͒. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases.

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“…The numerically observed critical exponents are: x = 1.0, ν ⊥ = 1.07 and ψ = .42 40 . Karevski et al 41 use a somewhat different numerical technique and find: x = 0.97, ν ⊥ = 1.25 and ψ = .5. In the light of the above arguments we expect also for the two-dimensional random contact process strong disorder scaling with the above exponents in Eq.…”

Section: Renormalization In Two Dimensionsmentioning

confidence: 99%

Absorbing state phase transitions with quenched disorder

2004

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Quenched disorder -in the sense of the Harris criterion -is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.

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Random quantum magnets with broad disorder distribution

Cited by 56 publications

References 23 publications

Random transverse field Ising model in dimensiond> 1: scaling analysis in the disordered phase from the directed polymer model

Random transverse field Ising model in dimensiond> 1: scaling analysis in the disordered phase from the directed polymer model

Renormalization group study of the two-dimensional random transverse-field Ising model

Absorbing state phase transitions with quenched disorder

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