This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition.The scaling theory of localisation and the Anderson model of localisation are briefly sketched.The finite size scaling method is described.Recent results for the critical exponents of the different symmetry classes are summarised.The importance of corrections to scaling are emphasised.A comparison with experiment is made, and a direction for future work is suggested.This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition.The scaling theory of localisation and the Anderson model of localisation are briefly sketched.The finite size scaling method is described.Recent results for the critical exponents of the different symmetry classes are summarised.The importance of corrections to scaling are emphasised.A comparison with experiment is made, and a direction for future work is suggested.

WORLD SCIENTIFIC eBooksJun 1, 20104 citations

An Investigation of Finite Size Scaling

E. Brézin

Current physics sources and commentsJan 1, 19882 citations

FINITE SIZE SCALING ANALYSIS OF THE ANDERSON TRANSITION

B. Krämer, A. MacKinnon, Tomi Ohtsuki +1 more

This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localization and the Anderson model of localization are briefly sketched. The finite size scaling method is described. Recent results for the critical exponents of the different symmetry classes are summarised. The importance of corrections to scaling are emphasised. A comparison with experiment is made, and a direction for future work is suggested.This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localization and the Anderson model of localization are briefly sketched. The finite size scaling method is described. Recent results for the critical exponents of the different symmetry classes are summarised. The importance of corrections to scaling are emphasised. A comparison with experiment is made, and a direction for future work is suggested.

arXiv:1004.0285International Journal of Modern Physics BMay 20, 201031 citations

Finite-size scaling: new results

Vladimir Privman A

Physica A Statistical Mechanics and its ApplicationsSep 1, 19919 citations

Finite-Size Scaling

A. P. Young

WORLD SCIENTIFIC eBooksAug 1, 20240 citations

Finite-Size Scaling and Correlation Lengths for Disordered Systems

Jennifer Chayes, L. Chayes, Daniel S. Fisher +1 more

For a large class of $d$ -dimensional disordered systems, we prove that if an appropriately defined finite-size scaling correlation length diverges at a nontrivial value of the disorder with an exponent $\ensuremath{\nu}$, then $\ensuremath{\nu}$ must satisfy the bound $\ensuremath{\nu}\ensuremath{\ge}\frac{2}{d}$. Given the assumption that such a correlation length can be defined, the result applies to, e.g., percolation, disordered magnets, and Anderson localization, both with and without interactions. For localization, this puts stringent constraints on scaling theories and interpretation of experiments.For a large class of $d$-dimensional disordered systems, we prove that if an appropriately defined finite-size scaling correlation length diverges at a nontrivial value of the disorder with an exponent $\ensuremath{\nu}$, then $\ensuremath{\nu}$ must satisfy the bound $\ensuremath{\nu}\ensuremath{\ge}\frac{2}{d}$. Given the assumption that such a correlation length can be defined, the result applies to, e.g., percolation, disordered magnets, and Anderson localization, both with and without interactions. For localization, this puts stringent constraints on scaling theories and interpretation of experiments.

Physical Review LettersDec 15, 1986674 citations

For a large class of

d

-dimensional disordered systems, we prove that if an appropriately defined finite-size scaling correlation length diverges at a nontrivial value of the disorder with an exponent $\ensuremath{\nu}$, then $\ensuremath{\nu}$ must satisfy the bound $\ensuremath{\nu}\ensuremath{\ge}\frac{2}{d}$. Given the assumption that such a correlation length can be defined, the result applies to, e.g., percolation, disordered magnets, and Anderson localization, both with and without interactions. For localization, this puts stringent constraints on scaling theories and interpretation of experiments.