The test of the finite-size scaling relations for the seven-dimensional Ising model on the Creutz cellular automaton

The seven-dimensional Ising model is simulated on the Creutz cellular autom aton using the finite-size lattices with the linear dimension 4 less than o r equal toL less than or equal to8. The exponents in the finite-size scalin g relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical temperature are computed to be 3.52(8) and 1.72(7 ) using 4 less than or equal toL less than or equal to8, respectively, whic h are in very good agreement with the theoretical predictions of 7/2 and 7/ 4. The finite-size scaling relation for the magnetic susceptibility at the infinite-lattice critical temperature is also valid for the maxima of the m agnetic susceptibilities of the finite-size lattices. The finite-size scali ng plots of the magnetic susceptibility and the order parameter verify the finite-size scaling relations about the infinite-lattice critical temperatu re. (C) 2001 Elsevier Science B.V. All rights reserved.