Non-universal exponents at the Anderson transition

✍ Scribed by Hideaki Obuse; Kousuke Yakubo

• Book ID: 104428595
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 121 KB
• Volume: 18
• Category: Article
• ISSN: 1386-9477
• DOI: 10.1016/s1386-9477(02)01015-9

✦ Synopsis

Fluctuations of the correlation dimension D2 describing multifractal properties of critical wavefunctions at the two-and three-dimensional Anderson transition points are studied by employing the forced-oscillator method and the box-counting procedure. We show that the width of the distribution function of D2 over disorder realizations remains ÿnite even in the thermodynamic limit. Similar results are obtained for the exponent characterizing quantum di usion at criticality. These imply that exponents deÿned at the critical point may not be universal. It is also shown that the scaling relation D2 = d (d is the spatial dimension) does not hold for individual samples, but is the case in a statistical sense.