Finite-size scaling in the ground state of spin-1/2antiferromagneticXXZrings

1987 ◽  
Vol 35 (4) ◽  
pp. 1877-1880 ◽  
Author(s):  
T. A. Kaplan ◽  
P. Horsch ◽  
J. Borysowicz
Keyword(s):  
Ground State ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling

Finite Size Scaling in the tt'-Hubbard Model and in BCS-Reduced Hubbard Models

1998 ◽  
Vol 09 (07) ◽  
pp. 943-985 ◽  
Author(s):  
W. Fettes ◽  
I. Morgenstern
Keyword(s):  
Hubbard Model ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Interaction Strength ◽  
Finite Size ◽  
Monte Carlo Algorithm ◽  
Finite Size Scaling ◽  
Hubbard Models ◽  
Size Scaling ◽  
Wave Symmetry

With the projector quantum Monte Carlo algorithm and the stochastic diagonalization it is possible to calculate the ground state of the Hubbard model for small finite clusters. Nevertheless the usual finite size scaling of the Hubbard model has problems of deducing the behavior of the infinite system correctly from the numerical data of small system sizes. Therefore we study the finite size scaling of the superconducting correlation functions in superconducting BCS-reduced Hubbard models to analyze the finite size behavior in small finite clusters. The ground state of the BCS-reduced Hubbard models is calculated with the stochastic diagonalization without any approximations. As result of these analyses we propose a new finite size scaling ansatz for the Hubbard model, which is able describe the finite size effects in a consistent way taking the corrections to scaling into account, which are dominant for weak interaction strength and small clusters. With this new finite size scaling ansatz it is possible to give evidence for superconductivity for all interaction strengths for both the attractive tt'-Hubbard model (with s-wave symmetry) and the repulsive tt'-Hubbard model (with dx2-y2-wave symmetry).

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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