The Finite-Size Scaling Study of Five-Dimensional Ising Model

The five-dimensional ferromagnetic Ising model is simulated on the Creutz cellular automaton algorithm using finite-size lattices with linear dimension 4 ≤ L ≤ 8. The critical temperature value of infinite lattice is found to be $T^{χ}$ (∞=8.7811 (1) using 4 ≤ L ≤ 8 which is also in very good agreement with the precise result. The value of the field critical exponent (δ =3.0067(2)) is good agreement with δ =3 which is obtained from scaling law of Widom. 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 2.5080 (1), 2.5005 (3) and 1.2501 (1) using 4 ≤ L ≤ 8, respectively, which are in very good agreement with the theoretical predictions of 5/2 and 5/4. The finite-size scaling plots of magnetic susceptibility and the order parameter verify the finite-size scaling relations about the infinite-lattice temperature.