Two-dimensional random-network model with symplectic symmetry

Minakuchi, Kei

doi:10.1103/physrevb.58.9627

Cited by 13 publications

(11 citation statements)

References 11 publications

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“…which is close to a numerical result ν = 2.746 ± 0.009 for a SU(2) model published recently [23], but considerably larger than ν = 2.05 ± 0.08 [6] and smaller than ν = 2.88 ± 0.15 as obtained in [21]. In contrast to the critical conductance and critical disorder, the critical exponent is sensitive to the system size as can be seen in figure 4.…”

Section: Critical Parameterssupporting

confidence: 90%

“…From our conductance data, the critical exponent ν was obtained for the first time using finite size scaling of the calculated electrical two-terminal conductance, which is, unlike the localization length, an easy way to measure physical quantity. With the finite size scaling analysis described in section (2.4), our estimation of the critical exponent gives ν = 2.8 ± 0.04, (11) which is close to a numerical result ν = 2.746 ± 0.009 for a SU(2) model published recently [23], but considerably larger than ν = 2.05 ± 0.08 [6] and smaller than ν = 2.88 ± 0.15 as obtained in [21]. In contrast to the critical conductance and critical disorder, the critical exponent is sensitive to the system size as can be seen in figure 4.…”

Section: Critical Parameterssupporting

confidence: 90%

“…It is well known that for Fermi energy E F ≈ 0, the Ando model exhibits a metalinsulator transition as a function of disorder at W = W c ≈ 5.8 [6,12]. The critical exponent for various 2d systems with symplectic symmetry has been estimated in numerous works using different numerical methods [12,15,20,21,22,14,23], leading to rather inconsistent results. The critical conductance was studied in [24].…”

Section: Hamiltonianmentioning

confidence: 99%

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Critical regime of two-dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates

Markoš

Schweitzer

2006

J. Phys. A: Math. Gen.

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The critical two-terminal conductance g c and the spatial fluctuations of critical eigenstates are investigated for a disordered two dimensional model of non-interacting electrons subject to spin-orbit scattering (Ando model). For square samples, we verify numerically the relation σ c = 1/[2π(2 − D(1))] e 2 /h between critical conductivity σ c = g c = (1.42 ± 0.005) e 2 /h and the fractal information dimension of the electron wave function, D(1) = 1.889 ± 0.001. Through a detailed numerical scaling analysis of the two-terminal conductance we also estimate the critical exponent ν = 2.80 ± 0.04 that governs the quantum phase transition.

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Section: Critical Parameterssupporting

confidence: 90%

Section: Critical Parameterssupporting

confidence: 90%

Section: Hamiltonianmentioning

confidence: 99%

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Critical regime of two-dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates

Markoš

Schweitzer

2006

J. Phys. A: Math. Gen.

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“…For example, in the presence of spin-orbit scattering, the estimates of the exponent ν in 2D are rather scattered e.g. 2.2 [33], 2.5 [47] and 2.8 [48,49], which can not be distinguished from the value of ν = 2.35 ± .03 obtained in the quantum Hall case. This may be due to the fact that the corrections to scaling is larger in 2D [47].…”

Section: Summary and Concluding Remarksmentioning

confidence: 87%

Review of recent progress on numerical studies of the Anderson transition

Ohtsuki¹,

Slevin²,

Kawarabayashi³

1999

Ann. Phys.

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A review of recent progress in numerical studies of the Anderson transition in three dimensional systems is presented. From high precision calculations the critical exponent ν for the divergence of the localization length is estimated to be ν = 1.57 ± 0.02 for the orthogonal universality class, which is clearly distinguished from ν = 1.43 ± 0.03 for the unitary universality class. The boundary condition dependences of some quantities at the Anderson transition are also discussed.

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“…There has been only very limited success in estimating the critical exponent with field theoretic methods [16,17]. In Table I we tabulate the estimates of the exponent reported in previous numerical studies [4,10,11,12,13,14,15]. There is considerable variation between these estimates.…”

mentioning

confidence: 99%

Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling

2002

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We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent nu for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyze the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent nu=2.73+/-0.02.

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Two-dimensional random-network model with symplectic symmetry

Cited by 13 publications

References 11 publications

Critical regime of two-dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates

Critical regime of two-dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates

Review of recent progress on numerical studies of the Anderson transition

Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling

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