scholarly journals Finite-size scaling at the jamming transition: Corrections to scaling and the correlation-length critical exponent

2011 ◽  
Vol 83 (3) ◽  
Author(s):  
Daniel Vågberg ◽  
Daniel Valdez-Balderas ◽  
M. A. Moore ◽  
Peter Olsson ◽  
S. Teitel
Keyword(s):  
Critical Exponent ◽  
Correlation Length ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Corrections To Scaling ◽  
Jamming Transition ◽  
Size Scaling

scholarly journals Finite-Size Scaling at the Jamming Transition

2012 ◽  
Vol 109 (9) ◽  
Author(s):  
Carl P. Goodrich ◽  
Andrea J. Liu ◽  
Sidney R. Nagel
Keyword(s):  
Finite Size ◽  
Finite Size Scaling ◽  
Jamming Transition ◽  
Size Scaling

Critical exponent of percolation conductivity by finite-size scaling

1983 ◽  
Vol 16 (16) ◽  
pp. L521-L527 ◽  
Author(s):  
M Sahimi ◽  
B D Hughes ◽  
L E Scriven ◽  
H T Davis
Keyword(s):  
Critical Exponent ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling

Field theory in a finite geometry: Finite size scaling

2019 ◽  
pp. 335-360
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Correlation Length ◽  
Zero Mode ◽  
Finite Size ◽  
System Size ◽  
Finite Geometry ◽  
Effective Field ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Statistical Systems

Computer simulations of critical statistical systems or quantum field theory models are performed with systems where sizes are finite. In transfer matrix calculations, all sizes but one are also finite. In systems where the correlation length is large, it is thus important to understand how the infinite size limit is reached. This problem is investigated in Chapter 19. RG equations allow proving the properties of universality and of finite size scaling. When the correlation length is larger than the linear system size, a phenomenon of dimensional reduction is observed. With periodic boundary conditions, fields have a zero mode. A local expansion generates an effective field theory for the zero mode.

scholarly journals FINITE SIZE SCALING AND RUNNING COUPLING CONSTANT IN CPN-1 MODELS

1998 ◽  
Vol 13 (06) ◽  
pp. 887-901
Author(s):  
EMANUELE MANFREDINI
Keyword(s):  
Correlation Length ◽  
Numerical Study ◽  
Finite Size ◽  
Perturbative Expansion ◽  
Finite Size Scaling ◽  
Coupling Constant ◽  
Size Scaling ◽  
Running Coupling ◽  
Running Coupling Constant ◽  
Conceptual Problems

In this work I present a numerical study of the Finite Size Scaling (FSS) of a correlation length in the framework of the CPN-1 model by means of the 1/N expansion. This study has been thought as preparatory to the application of FSS to the measure on the lattice of a new coupling constant fx(1/R), defined in terms or rectangular Wilson loops. I give also a perturbative expansion of fx(1/R) in powers of the corresponding coupling constant in the [Formula: see text] scheme together with some preliminary numerical results obtained from the Polyakov ratio and I point out the conceptual problems that limit this approach.

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.

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