The effect of the number of simulations on the exponents obtained by 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 lattice with the linear dimension 4⩽ L⩽8. 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 3.544(24), 3.505(55), 3.501(52), 1.78(64), 1.77(38), 1.76(46) and 0.02(11), 0.01(17), 0.01(16) using 4⩽ L⩽8 for 7,14 and 21 independent simulations, respectively. As the number of independent simulations increase, exponents are in very good agreement with the theoretical predictions of 7/2, 7/4 and 0, respectively. The values for the critical temperature of infinite lattice 12.870(12), 12.870(10), 12.869(3) and 12.871(15), 12.871(5), 12.871(5) are obtained from the straight line fit of the magnetic susceptibility maxima and the specific heat using 4⩽ L⩽8 for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are in very good agreement with the more precise value of 12.86902(33).