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

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, 7 4 , 1, 5 2 , 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.