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

Abstract

The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4 <= L <= 22. The exponents in the finite-size scaling relations for the order parameter, the magnetic susceptibility at the finite-lattice critical temperature and the specific heat at the infinite-lattice critical temperature are computed to be beta = 0.5072(58), gamma = 1.0287(56) and alpha = -0.096(17), respectively, which are consistent with the renormalization group prediction of beta = 0.5, gamma = 1 and alpha = 0. The critical temperatures for the infinite lattice are found to be T-c(chi) = 6.6824(5) and T-c(C) = 6.6736(27), which are also consistent with the precise results.