  Role of range of interactions in a model of charged particles diffusing on a
two-dimensional lattice is studied. We investigate, via Monte Carlo
simulations, three models. In the first one interactions are restricted to
nearest neighbors, in the second one we add (weaker) interactions to second
nearest neighbors. In the third model interactions are extended as far as the
half the size of the system. The strength of these interactions falls off with
the distance. We show that for static properties, such as asymptotic spatial
patterns or the order parameter, the results of the first and third models are
very close. Dynamic characteristics, like mean square displacement, average
cluster size and average energy as functions of time show larger differences
among the three models. Origins of these differences are pointed out and
discussed.
