A mean-field approximation scheme containing the spatial parameter and its application to a surface-reaction-like cellular automaton model

Using an AB₂ surface-reaction-like cellular automaton model, we present a modified mean-field approximation scheme for describing some dynamic lattice models, in which a lattice freedom parameter N is introduced as a variable. We obtain the phase diagrams of the example model for linear, hexagonal, square and triangular lattices, and we reveal a second-order phase transition which has not been found using traditional approaches.