scholarly journals Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions

2015 ◽  
Vol 91 (18) ◽  
Author(s):  
László Ujfalusi ◽  
Imre Varga
Keyword(s):  
Finite Size ◽  
Three Dimensions ◽  
Finite Size Scaling ◽  
Anderson Transition ◽  
Size Scaling ◽  
Symmetry Classes

scholarly journals FINITE SIZE SCALING ANALYSIS OF THE ANDERSON TRANSITION

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1841-1854 ◽  
Author(s):  
B. Kramer ◽  
A. MacKinnon ◽  
T. Ohtsuki ◽  
K. Slevin
Keyword(s):  
Finite Size ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Corrections To Scaling ◽  
Anderson Transition ◽  
The Past ◽  
Size Scaling ◽  
Symmetry Classes ◽  
Comparison With Experiment ◽  
Future Work

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.

Finite-size scaling for the Bose condensate

1985 ◽  
Vol 63 (3) ◽  
pp. 358-365 ◽  
Author(s):  
Surjit Singh ◽  
R. K. Pathria
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Bose Condensate ◽  
Finite Size ◽  
Dirichlet Boundary Conditions ◽  
Three Dimensions ◽  
Bose System ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Temperature Variable

Following the approach of Barber and Fisher, we formulate a finite-size scaling theory for the Bose condensate. Using bulk results as input, we make a number of predictions for the behaviour of the condensate fraction f0(L, T) in an ideal Bose system confined to a hypercube, of side L, in d dimensions. A comparison is made with analytical results for a system in three dimensions under a variety of boundary conditions. While the standard temperature variable t[= (T – Tc)/Tc] is appropriate in the case of periodic and antiperiodic boundary conditions, the use of a shifted variable t[= t – ε(L), where ε(L) = O(L−1 In L)] is essential in the case of Neumann and Dirichlet boundary conditions. Nonetheless, in each case, the predictions of the scaling formulation are fully borne out. Finally, the formulation is extended (i) to include the so-called surface condensate, and (ii) to cover all temperature down to 0 K.

scholarly journals Finite-size scaling of the level compressibility at the Anderson transition

2002 ◽  
Vol 27 (3) ◽  
pp. 399-407 ◽  
Author(s):  
M.L. Ndawana ◽  
R.A. Römer ◽  
M. Schreiber
Keyword(s):  
Finite Size ◽  
Finite Size Scaling ◽  
Anderson Transition ◽  
Size Scaling

scholarly journals FINITE SIZE SCALING ANALYSIS OF THE ANDERSON TRANSITION

2010 ◽  
pp. 347-360 ◽  
Author(s):  
B. Kramer ◽  
A. MacKinnon ◽  
T. Ohtsuki ◽  
K. Slevin
Keyword(s):  
Finite Size ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Anderson Transition ◽  
Size Scaling
Sign in / Sign up

Export Citation Format

Share Document