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Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition

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Macleans L. Ndawana, Rudolf A. Roemer, Michael Schreiber

Disordered Systems and Neural Networks · Submitted 1 Feb 2004

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We study the dependence of the localization-length exponent $\nu$ on the correlation-strength exponent $\alpha$. % For fixed disorder $W$, there is a critical $\alpha_{\rm c}$, such that for $\alpha < \alpha_{\rm c}$, $\nu=2/\alpha$ and for $\alpha > \alpha_{\rm c}$, $\nu$ remains that of the uncorrelated system in accordance with the extended Harris criterion.

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arXiv IDcond-mat/0402018 (version 1)
Pith IDHMK2CJWL, Pith's permanent record of this paper and its review
CitationMacleans L. Ndawana, Michael Schreiber, Rudolf A. Roemer. "Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition." arXiv:cond-mat/0402018 (2004). https://pith.science/paper/HMK2CJWL
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,748 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.49 · randomized assignment 0.01 · states quantitative result 0.81 · compares with prior results 0.79 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We investigate the three-dimensional Anderson model of localization via a modified transfer-matrix method in the presence of scale-free diagonal disorder characterized by a disorder correlation function $g(r)$ decaying asymptotically as $r^{-\alpha}$. We study the dependence of the localization-length exponent $\nu$ on the correlation-strength exponent $\alpha$. % For fixed disorder $W$, there is a critical $\alpha_{\rm c}$, such that for $\alpha < \alpha_{\rm c}$, $\nu=2/\alpha$ and for $\alpha > \alpha_{\rm c}$, $\nu$ remains that of the uncorrelated system in accordance with the extended Harris criterion. At the band center, $\nu$ is independent of $\alpha$ but equal to that of the uncorrelated system. The physical mechanisms leading to this different behavior are discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We investigate the three-dimensional Anderson model of localization via a modified transfer-matrix method in the presence of scale-free diagonal disorder characterized by a disorder correlation function $g(r)$ decaying asymptotically as $r^{-\alpha}$. contribution 0.66 0.92 0.04 asserted 0.88
s1 We study the dependence of the localization-length exponent $\nu$ on the correlation-strength exponent $\alpha$. % For fixed disorder $W$, there is a critical $\alpha_{\rm c}$, such that for $\alpha < \alpha_{\rm c}$, $\nu=2/\alpha$ and for $\alpha > \alpha_{\rm c}$, $\nu$ remains that of the uncorrelated system in accordance with the extended Harris criterion. result 0.90 0.77 0.72 asserted 0.86
s2 At the band center, $\nu$ is independent of $\alpha$ but equal to that of the uncorrelated system. result 1.00 0.87 0.17 asserted 1.00
s3 The physical mechanisms leading to this different behavior are discussed. interpretation 0.91 0.50 0.03 unclear 0.77

What kind of paper the classifier reports this is: simulation study 0.98 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We investigate the three-dimensional Anderson model of localization via a modified transfer-matrix method in the presence of scale-free diagonal disorder characterized by a disorder correlation function $g(r)$ decaying asymptotically as $r^{-\alpha}$. We study the dependence of the localization-length exponent $\nu$ on the correlation-strength exponent $\alpha$. % For fixed disorder $W$, there is a critical $\alpha_{\rm c}$, such that for $\alpha < \alpha_{\rm c}$, $\nu=2/\alpha$ and for $\alpha > \alpha_{\rm c}$, $\nu$ remains that of the uncorrelated system in accordance with the extended Harris criterion. At the band center, $\nu$ is independent of $\alpha$ but equal to that of the uncorrelated system. The physical mechanisms leading to this different behavior are discussed.

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