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The Test of a New Critical Exponent Ϙ by Using Ising Model on the Creutz Cellular Automaton

100%
Merdan Z., Gokbel-Keklikoglu D.
Acta Physica Polonica A
|
2018
|
vol. 133
|
issue 5
1200-1204
EN
Above the upper critical dimension d_{c} the Ising model is simulated on the Creutz cellular automaton. The values of a new critical exponent Ϙ are obtained by using the simulations for the order parameter and the magnetic susceptibility. At d=4,5,6,7,8, the values of the new critical exponent Ϙ are 0.9904(16), 1.2721(2), 1.4806(24), 1.7626(17), 1.9997(50) for the order parameter, respectively, while those 1.0415(13), 1.2987(27), 1.5133(1), 1.7741(1), 2.0133(28) are for the magnetic susceptibility in the same order. The computed values of the new critical exponent Ϙ are in agreement with theoretical values.
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The Finite-Size Scaling Study of Five-Dimensional Ising Model

81%
Merdan Z., Aras N., Kürkçü C.
Acta Physica Polonica A
|
2016
|
vol. 129
|
issue 6
1100-1104
EN
The five-dimensional ferromagnetic Ising model is simulated on the Creutz cellular automaton algorithm using finite-size lattices with linear dimension 4 ≤ L ≤ 8. The critical temperature value of infinite lattice is found to be T^{χ} (∞=8.7811 (1) using 4 ≤ L ≤ 8 which is also in very good agreement with the precise result. The value of the field critical exponent (δ =3.0067(2)) is good agreement with δ =3 which is obtained from scaling law of Widom. The exponents in the finite-size scaling relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical temperature are computed to be 2.5080 (1), 2.5005 (3) and 1.2501 (1) using 4 ≤ L ≤ 8, respectively, which are in very good agreement with the theoretical predictions of 5/2 and 5/4. The finite-size scaling plots of magnetic susceptibility and the order parameter verify the finite-size scaling relations about the infinite-lattice temperature.
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