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

Abstract

The seven-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4⩽ L⩽8. 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 3.52(8) and 1.72(7) using 4⩽ L⩽8, respectively, which 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 magnetic susceptibilities of the finite-size lattices. The finite-size scaling plots of the magnetic susceptibility and the order parameter verify the finite-size scaling relations about the infinite-lattice critical temperature.