NDLI: The Effect of the Number of Simulations on the Exponents Obtained by Finite-Size Scaling Relations of the Order Parameter and the Magnetic Susceptibility for the Four-Dimensional Ising Model on the Creutz Cellular Automaton

Content Provider	Springer Nature Link
Author	Merdan, Z. Güzelsoy, E.
Copyright Year	2011
Abstract	The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4≤L≤8. The exponents in the finite-size scaling relations for the order parameter and the magnetic susceptibility at the finite-lattice critical temperature are computed to be β=0.49(7), β=0.49(5), β=0.50(1) and γ=1.04(4), γ=1.03(4), γ=1.02(4) for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are consistent with the renormalization group predictions of β=0.5 and γ=1. The values for the critical temperature of the infinite lattice T $_{ c }$(∞)=6.6788(65), T $_{ c }$(∞)=6.6798(69), T $_{ c }$(∞)=6.6802(70) are obtained from the straight-line fit of the magnetic susceptibility maxima using 4≤L≤8 for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are in very good agreement with the series expansion results of T $_{ c }$(∞)=6.6817(15), T $_{ c }$(∞)=6.6802(2), the dynamic Monte Carlo result of T $_{ c }$(∞)=6.6803(1), the cluster Monte Carlo result of T $_{ c }$(∞)=6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm result of T $_{ c }$(∞)=6.6802632±5×10$^{−5}$.
Starting Page	1621
Ending Page	1631
Page Count	11
File Format	PDF
ISSN	00207748
Journal	International Journal of Theoretical Physics
Volume Number	51
Issue Number	5
e-ISSN	15729575
Language	English
Publisher	Springer US
Publisher Date	2011-12-07
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Ising model Cellular automata Critical exponents Finite-size scaling Quantum Physics Theoretical, Mathematical and Computational Physics Elementary Particles, Quantum Field Theory Physics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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