Lattice models with nearest-neighbor interactions have been used extensively to model a wide variety of systems and phenomena, including the lattice gas, binary liquid solutions, order-disorder phase transitions, ferromagnetism, and antiferromagnetism.
[1] Most calculations of correlation functions for nonrandom configurations are based on statistical mechanical techniques, which lead to equations that usually need to be solved numerically.
In 1944 Onsager[3] was able to get an exact solution to a two-dimensional (2D) lattice problem at the critical density.
[4] Over the last ten years, Aranovich and Donohue have developed lattice density functional theory (LDFT) based on a generalization of the Ono-Kondo equations to three-dimensions, and used the theory to model a variety of physical phenomena.
Although this approach is known to give only qualitative information about the thermodynamic behavior of a system, it provides important insights about the mechanisms of various complex phenomena such as phase transition,[5][6][7] aggregation,[8] configurational distribution,[9] surface-adsorption,[10][11] self-assembly, crystallization, as well as steady state diffusion.