Corrections to finite-size-scaling laws and convergence of transfer-matrix methods

1985 ◽  
Vol 31 (5) ◽  
pp. 3069-3083 ◽  
Author(s):  
J. M. Luck
Keyword(s):  
Transfer Matrix ◽  
Scaling Laws ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Matrix Methods ◽  
Size Scaling

SCALING LAW OF SUPERFLUID–INSULATOR TRANSITION IN THE 1D BOSE–HUBBARD MODEL

2012 ◽  
Vol 26 (04) ◽  
pp. 1250014 ◽  
Author(s):  
SHI-JIAN GU ◽  
JUNPENG CAO ◽  
SHU CHEN ◽  
HAI-QING LIN
Keyword(s):  
Hubbard Model ◽  
Critical Point ◽  
Scaling Laws ◽  
Scaling Law ◽  
Finite Size ◽  
Superfluid Density ◽  
Insulator Transition ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Size Scaling

The finite size scaling behavior of superfluid–insulator transition in the one-dimensional Bose–Hubbard model is studied. It is shown that the superfluid density of the system with finite size has a maximum at a certain interaction Um and the derivative of superfluid density has a minimum at a certain interaction Ud. The critical point Uc can be quantified by the scaling analysis of either Um or Ud. The transition point Um tends to the critical point Uc from the region of U < Uc, while the Ud tends to the Uc from the region of U > Uc. The transition points Um and Ud satisfy different finite size scaling laws and have the different critical exponents. The divergence speed of the superfluid density is much smaller than that of its derivative at the critical point.

scholarly journals STRUCTURE CONSTANT OF THE YANG–LEE EDGE SINGULARITY

2008 ◽  
Vol 22 (27) ◽  
pp. 4793-4797
Author(s):  
TOMASZ WYDRO ◽  
JOHN F. McCABE
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Ising Model ◽  
Transfer Matrix ◽  
Finite Size ◽  
Structure Constant ◽  
Finite Size Scaling ◽  
Edge Singularity ◽  
Conformal Field ◽  
Size Scaling

This paper studies the Yang–Lee singularity of the 2-dimensional Ising model on the cylinder via transfer matrix and finite-size scaling techniques. These techniques enable a measurement of the 2-point and 3-point correlations and a comparison of a measurement of a corresponding universal amplitude with a prediction for the amplitude from the (A4, A1) minimal conformal field theory.

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.

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