Regensburg 2010 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 20: Phase Transitions and Critical Phenomena I

DY 20.7: Vortrag

Mittwoch, 24. März 2010, 16:00–16:15, H47

Critical exponents of the three-dimensional Anderson transition from multifractal analysis — •Louella Judy Vasquez¹, Alberto Rodriguez¹, Rudolf Römer¹, and Keith Slevin² — ¹Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry CV47AL, United Kingdom — ²Department of Physics, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan

We use high-precision, large system-size wavefunction data to analyse the scaling properties of the multifractal spectra around the disorder-induced three-dimensional Anderson transition in order to extract the critical exponent ν of the localisation length. We study the scaling law around the critical point of the generalized inverse participation ratios P_q=<|ψ_i|>² and the singularity exponent α₀, defined as the position of the maximum of the multifractal spectrum, as functions of the degree of disorder, the system size, and the box-size used to coarse-grained the wavefunction amplitudes. The values of α₀ are calculated using a new method entirely based on the statistics of the wavefunction intensities [Phys. Rev. Lett. 102, 106406 (2009)]. Using finite size scaling analysis, we find agreement with the values of ν obtained from transfer matrix calculations.