Percolation, Renormalization and Quantum Hall Transition
作者： Rudolf A. Römer
DOI: 10.1007/978-3-662-04804-7_17
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摘要: In this article, I give a pedagogical introduction and overview of percolation theory. Special emphasis will be put on the review some most prominent algorithms devised to study numerically. The real-space renormalization group treatment problem is then discussed. As rather novel application approach percolation, recent results using similar ideas that have been applied quantum Hall transition.
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J. M. Hammersley, Percolation processes. II. The connective constant Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 53, pp. 642- 645 ,(1957) , 10.1017/S0305004100032692
R. B. Laughlin, Quantized Hall conductivity in two dimensions Physical Review B. ,vol. 23, pp. 5632- 5633 ,(1981) , 10.1103/PHYSREVB.23.5632
P. Kleban, R. M. Ziff, EXACT RESULTS AT THE TWO-DIMENSIONAL PERCOLATION POINT Physical Review B. ,vol. 57, ,(1998) , 10.1103/PHYSREVB.57.R8075
A. B. Harris, T. C. Lubensky, W. K. Holcomb, C. Dasgupta, Renormalization-Group Approach to Percolation Problems. Physical Review Letters. ,vol. 35, pp. 327- 330 ,(1975) , 10.1103/PHYSREVLETT.35.327
Paul N. Suding, Robert M. Ziff, Site percolation thresholds for Archimedean lattices. Physical Review E. ,vol. 60, pp. 275- 283 ,(1999) , 10.1103/PHYSREVE.60.275
S. Koch, R. J. Haug, K. v. Klitzing, K. Ploog, Experiments on scaling in AlxGa1-xAs/GaAs heterostructures under quantum Hall conditions. Physical Review B. ,vol. 43, pp. 6828- 6831 ,(1991) , 10.1103/PHYSREVB.43.6828
R M Ziff, B Sapoval, The efficient determination of the percolation threshold by a frontier-generating walk in a gradient Journal of Physics A. ,vol. 19, pp. 010- ,(1986) , 10.1088/0305-4470/19/18/010
M. Janssen, O. Viehweger, U. Fastenrath, J. Hajdu, Steven M. Girvin, Introduction to the Theory of the Integer Quantum Hall Effect Physics Today. ,vol. 48, pp. 60- 61 ,(1995) , 10.1063/1.2808136
R. T. F. van Schaijk, A. de Visser, S. M. Olsthoorn, H. P. Wei, A. M. M. Pruisken, Probing the plateau-insulator quantum phase transition in the quantum hall regime Physical Review Letters. ,vol. 84, pp. 1567- 1570 ,(2000) , 10.1103/PHYSREVLETT.84.1567
P. L. Leath, Cluster size and boundary distribution near percolation threshold Physical Review B. ,vol. 14, pp. 5046- 5055 ,(1976) , 10.1103/PHYSREVB.14.5046