Self-consistent Ornstein-Zernike approximation compared with Monte Carlo results for two-dimensional lattice gases

The self-consistent Ornstein-Zernike approach (SCOZA) is solved numerically for a lattice gas or Ising model on the simple square lattice in two dimen sions. Interactions of varying range are considered, and the results are co mpared with corresponding simulation ones. We focus especially upon the loc ation of the critical temperature T-c which is identified with the maximum of the specific heat. The maximum remains finite for the finite-sized simul ation sample and also for SCOZA, which treats infinite lattices in two dime nsions as though they were finite samples. We also investigate the influenc e of the precise form of the interaction, first using an interaction that e xtends the nearest-neighbor case in a simple way and then considering the s quare-well interactions used in the simulations. We find that the shift in T-c away from its mean-field value is governed primarily by the range of in teraction. Other specific features of the interaction leave a smaller influ ence but are relevant to a quantitative comparison with simulations. The SC OZA yields accurate results, and the influence of the precise form of the a ttractive interaction plays a significant role in SCOZA's success. (C) 2001 American Institute of Physics.