Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Phase Transitions and Critical Phenomena

DY 31.13: Topical Talk

Friday, March 30, 2012, 13:00–13:30, MA 004

Multifractal fluctuations and Scaling at the three-dimensional Anderson transition — •Alberto Rodriguez^1,2, Louella J. Vasquez³, Keith Slevin⁴, and Rudolf A. Roemer² — ¹Phisikalisches Institut, Albert-Ludwigs Universität Freiburg, 79104, Freiburg, Germany — ²Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, UK — ³Institute of Advanced Study, Complexity Science Centre and Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK — ⁴Department of Physics, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan

We analyze the multifractal properties of the critical wavefunctions at the disorder-induced three-dimensional metal-insulator transition (MIT), and we discuss the relation between the multifractal spectrum and the probability density function (PDF) of wavefunction intensities at criticality. A new PDF-based characterization of the MIT is presented and emphasized in connection with latest experimental observations of critical phenomena. Furthermore, we describe a new multifractal finite size scaling (MFSS) procedure that permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simulations of system sizes up to L³=120³ and involving nearly 10⁶ independent wavefunctions have yielded unprecedented precision for the critical disorder W_c=16.530(16.524,16.536) and the critical exponent ν=1.590(1.579,1.602). This formalism is applicable to any continuous phase transition exhibiting multifractal fluctuations in the vicinity of the critical point.