  It has been previously shown that one can use the ME methodology (Caticha
Giffin 2006) to reproduce a mean field solution for a simple fluid (Tseng
2004). One could easily use the case of a simple ferromagnetic material as
well. The drawback to the mean field approach is that one must assume that all
atoms must all act the same. The problem becomes more tractable when the agents
are only allowed to interact with their nearest neighbors and can be in only
two possible states. The easiest case being an Ising model. The purpose of this
paper is to illustrate the use of the ME method as an approximation tool. The
paper show a simple case to compare with the traditional mean field approach.
Then we show two examples that lie outside of traditional methodologies. These
cases explore a ferromagnetic material with defects. The main result is that
regardless of the case, the ME method provides good approximations for each
case which would not otherwise be possible or at least well justified.
