The test of the finite-size scaling relations of the Ising models in seven and eight dimensions on the Creutz cellular automaton

Z. Merdan, A. Duran, D. Atille, G. Mülazimogˇlu and A. Günen

Physica A: Statistical Mechanics and its Applications, 2006, vol. 366, issue C, 265-272

Abstract: The Ising models in seven and eight dimensions are simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4⩽L⩽8. Three different finite-size exponents for the order parameter near the curie point are computed to be 1.74 (3), 0.95 (2), 2.42 (5), 1.99 (19), 0.96 (1) and 2.95 (11) for d=7 and d=8 dimensions, respectively. The obtained results are in good agreement with the theoretical predictions, 74, 1, 52, 2, 1, 3 for d=7 and 8 dimensions, respectively. The exponent in the finite-size scaling relation for the magnetic suscebtibility at the infinite-lattice critical temperature is computed to be 4.03 (9) using 4⩽L⩽8, which is in very good agreement with the theoretical prediction of 4 for d=8 dimension. The finite-size scaling relation for the magnetic susceptibility at the infinite-lattice critical temperature is also valid for the maxima of the magnetic susceptibilities of the finite-size lattices. The finite-size scaling plots of the order parameter and the magnetic susceptibility verify the finite-size scaling relations about the infinite-lattice critical temperature.

Keywords: Ising models; Cellular automaton; Critical exponents (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:366:y:2006:i:c:p:265-272

DOI: 10.1016/j.physa.2005.10.035

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