A method for regular improvement of the mean field approximations for latti
ce systems is proposed. The method requires transcription of the initial la
ttice to a new lattice of complex sites each representing the states of sev
eral initial sites. This approach is valuable for the description of many-p
article distributions on the lattice. The validity of this approach is test
ed by comparison of the coexistence curve, the concentration dependence of
the probabilities for two lattice sites to be vacant and the jump diffusion
coefficients for two-dimensional square lattice gas with Monte Carlo simul
ation data. (C) 1999 Elsevier Science B.V. All rights reserved.