Multifractal finite-size scaling and universality at the Anderson transition

被引：150

作者：

Rodriguez, Alberto ^{[1
,2
,3
]}

Vasquez, Louella J. ^{[4
,5
]}

Slevin, Keith ^{[6
]}

Roemer, Rudolf A. ^{[1
,2
]}

机构：

[1] Univ Warwick, Dept Phys, Coventry CV4 7AL, W Midlands, England

[2] Univ Warwick, Ctr Comp Sci, Coventry CV4 7AL, W Midlands, England

[3] Univ Salamanca, Dept Fis Fundamental, E-37008 Salamanca, Spain

[4] Univ Warwick, Inst Adv Study, Complex Sci Ctr, Coventry CV4 7AL, W Midlands, England

[5] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

[6] Osaka Univ, Dept Phys, Grad Sch Sci, Osaka 5600043, Japan

来源：

PHYSICAL REVIEW B | 2011年 / 84卷 / 13期

基金：

英国工程与自然科学研究理事会;

关键词：

METAL-INSULATOR-TRANSITION; CRITICAL-BEHAVIOR; ANISOTROPIC SYSTEMS; CRITICAL EXPONENT; WAVE-FUNCTIONS; DIMENSIONS; LOCALIZATION; STATES; MODEL;

D O I：

10.1103/PhysRevB.84.134209

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We describe a new multifractal finite-size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simulations of system sizes up to L-3 = 120(3) and involving nearly 10(6) independent wave functions have yielded unprecedented precision for the critical disorder W-c = 16.530(16.524,16.536) and the critical exponent nu = 1.590(1.579,1.602). We find that the multifractal exponents Lambda(q) exhibit a previously predicted symmetry relation and we confirm the nonparabolic nature of their spectrum. We explain in detail the MFSS procedure first introduced in our Letter [Phys. Rev. Lett. 105, 046403 (2010)] and, in addition, we show how to take account of correlations in the simulation data. The MFSS procedure is applicable to any continuous phase transition exhibiting multifractal fluctuations in the vicinity of the critical point.

引用

页数：16

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