  In this paper the percolation of monomers on a square lattice is studied as
the particles interact with either repulsive or attractive energies. By means
of a finite-size scaling analysis, the critical exponents and the scaling
collapsing of the fraction of percolating lattice are found. A phase diagram
separating a percolating from a non-percolating region is determined. The main
features of the phase diagram are discussed in terms of simple considerations
related to the interactions present in the problem. The influence of the phase
transitions occurring in the system is reflected by the phase diagram. In
addition, a scaling treatment maintaining constant the surface coverage and
varying the temperature of the system is performed. In all the considered
cases, the universality class of the model is found to be the same as for the
random percolation model.

Statistical Mechanics