Monte Carlo Computations on the Ising Model. The Body-Centered Cubic Lattice

Abstract

The Monte Carlo method of computation has been used to obtain some equilibrium properties of bcc binary solid solutions whose atoms interact according to the Ising model. Four cases have been treated: (a) N=128, c=½, (b) N=1024, c=½, (c) N=1024, c=3/8, and (d) N=1024, c=¼ (N being the total number of atoms and c the fraction of one kind.) In all cases the heat capacity has a well‐defined maximum. At the equiatomic composition, the height of this maximum is greater in the larger crystal. Discontinuities in thermodynamic properties were not observed, and it seems reasonable that the order‐disorder transition in an infinite crystal would be characterized by an infinite heat capacity as calculated by Onsager and others for two‐dimensional crystals. Comparison of the results with experimental properties of β‐CuZn suggests a remarkable applicability of the Ising model to this system. The potentialities and limitations of the Monte Carlo method for systems with phase transitions are discussed.