Book review: Finite size scaling and numerical simulation of statistical systems

1992 ◽  
Vol 69 (5-6) ◽  
pp. 1151-1151
Author(s):  
Dennis C. Rapaport
Keyword(s):  
Numerical Simulation ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Statistical Systems

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 A NEW APPROACH TO DYNAMIC FINITE-SIZE SCALING

2003 ◽  
Vol 14 (07) ◽  
pp. 945-954 ◽  
Author(s):  
MEHMET DİLAVER ◽  
SEMRA GÜNDÜÇ ◽  
MERAL AYDIN ◽  
YİĞİT GÜNDÜÇ
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Taylor Series Expansion ◽  
Scaling Behavior ◽  
Dynamic Scaling ◽  
Finite Size Scaling ◽  
New Approach ◽  
Size Scaling ◽  
Dynamic Exponent ◽  
Good Agreement

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

scholarly journals On the use of finite-size scaling to measure spin-glass exponents

2003 ◽  
Vol 36 (21) ◽  
pp. 5699-5706 ◽  
Author(s):  
A C Carter ◽  
A J Bray ◽  
M A Moore
Keyword(s):  
Spin Glass ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling
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