The effect of the increase of linear dimensions on exponents obtained by finite-size scaling relations for the six-dimensional Ising model on the Creutz cellular automaton

• Published in: Applied mathematics and computation Vol. 167; no. 1; pp. 212 - 224
• Main Authors: Merdan, Z., Bayırlı, M.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 05.08.2005
• Subjects: Cellular automata; Critical exponents; Ising models; Ising models; Critical exponents; Cellular automata
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2004.06.092

The six-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 ⩽ L ⩽ 12. The exponents in the finite-size scaling relations for the magnetic susceptibility, the order parameter and the specific heat at the infinite-lattice critical temperature are computed to be 3.00(12), 1.49(12) and 0.001(68) using 4 ⩽ L ⩽ 10, respectively, which are in very good agreement with the theoretical predictions of 6 2 , 6 4 and 0. The critical temperature for the infinite lattice is found to be 10.8347(52) using 6 ⩽ L ⩽ 12 which is also in very good agreement with the precise results. The finite-size scaling relation for magnetic susceptibility at the infinite-lattice critical temperature is also valid for the maxima of magnetic susceptibilities of the finite-size lattices. The finite-size scaling plots of magnetic susceptibility, the order parameter and the specific heat verify the finite-size scaling relations about the infinite-lattices temperature.