Monte Carlo simulation of the fcc antiferromagnetic Ising model

Monte Carlo methods are employed to measure the internal energy, sublattice magnetization, and spin-spin correlation function of the fcc antiferromagnetic Ising model as a function of temperature. The internal energy of both the ordered and disordered phases is fitted by appropriate series expansions, and the free energy is obtained analytically from the series. The ordering transition is seen to be of first order with a transition temperature of 1.736±{}0.001 in units of the nearest-neighbor coupling J. These results are compared with earlier approximations of the model, in particular, the low-temperature series expansion and the Kikuchi tetrahedron approximation, and other Monte Carlo results. The spin-spin correlation function was measured in the disordered phase up to eight lattice spacings in the [100] direction. The correlation length at the transition is found to be ~2.5a. The behavior of the correlation length is approximately mean-field-like.