  We analyze diffusion of particles on a two dimensional square lattice. Each
lattice site contains an arbitrary number of particles. Interactions affect
particles only in the same site, and are macroscopically represented by the
excess chemical potential. In a recent work, a general expression for
transition rates between neighboring cells as functions of the excess chemical
potential was derived. With transition rates, the mean field tracer
diffusivity, $D^\text{MF}$, is immediately obtained. The tracer diffusivity, $D
= D^\text{MF} f$, contains the correlation factor $f$, representing memory
effects. An analysis of the joint probability of having given numbers of
particles at different sites when a force is applied to a tagged particle
allows an approximate expression for $f$ to be derived. The expression is
applied to soft core interaction (different values for the maximum number of
particles in a site are considered) and extended hard core.
