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

Abstract

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(chi) (infinity) = 6; 680(1) obtained for h = 0 agrees well with the values T-c(infinity) approximate to 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 not equal 0 in the literature. The value of the field critical exponent (delta = 3.0136(3)) is in good agreement with delta = 3 which is obtained from scaling law of Widom. In spite of the finite-size scaling relations of vertical bar M-L(t)vertical bar and chi(L)(t) for 0 <= h <= 0.001 are verified; however, in the cases of 0.0025 <= h <= 0.1 they are not verified. (C) 2014 AIP Publishing LLC.