Study of four dimensional Ising model (18,20,22) and (18,20,22) lattices using Creutz cellular automaton

The four-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using three- and four- bit demons near the infinite-lattice critical temperature with the linear dimensions L=18,20 and 22. The critical temperature values of infinitive lattice and the critical exponents for the order parameter, the magnetic susceptibility and the specific heat are obtained from the results of simulations by using finite-size scaling relations. On the other hand the order parameter probability distribution for four dimensional Ising Model are calculated at the critical temperature. The finite size scaling relation for the order parameter probability distiribution is tested and verified nümerically by the Creutz Cellular Automaton simulation. The constants of the analytical function are estimated by fitting it to probability function obtained numerically at the finite size critical point. For the large finite size, the analytical function is described the universal shape of order parameter probability distiribution function.