The finite-size scaling study of four-dimensional Ising model in the presence of external magnetic field

Анотація

The four-dimensional ferromagnetic Ising model in external magnetic field 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, T_c^c (∞) = 6.680(1) obtained for h = 0 agrees well with the values T_c (∞) ≈ 6.68 obtained previously using different methods. Moreover, h = 0.00025 in our work also agrees with all the results obtained from h = 0 in the literature. However, there are no works for h ≠ 0 in the literature. The value of the field critical exponent (d = 3.0136(3)) is in good agreement with d = 3 which is obtained from scaling law of Widom. In spite of the finite-size scaling relations of |M_L(t)| and c_L(t) for 0 ≤ h ≤ 0.001 are verified; however, in the cases of 0.0025 ≤ h ≤ 0.1 they are not verified.