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 Running coupling constant and correlation length from Wilson loops

1995 ◽  
Vol 349 (4) ◽  
pp. 499-503 ◽  
Author(s):  
Massimo Campostrini ◽  
Paolo Rossi ◽  
Ettore Vicari
Keyword(s):  
Correlation Length ◽  
Wilson Loops ◽  
Coupling Constant ◽  
Running Coupling ◽  
Running Coupling Constant

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 The crossover from first to second-order finite-size scaling: a numerical study

1994 ◽  
Vol 4 (7) ◽  
pp. 1027-1048 ◽  
Author(s):  
Christian Borgs ◽  
P. E.L. Rakow ◽  
Stefan Kappler
Keyword(s):  
Numerical Study ◽  
Finite Size ◽  
Second Order ◽  
Finite Size Scaling ◽  
Size Scaling
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