  The renormalized charge of a simple two-dimensional model of colloidal
suspension was determined by solving the hypernetted chain approximation and
Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic
behavior of the correlations functions is used to define the effective
interactions between the components of the system and these effective
interactions were compared to those derived from the Poisson-Boltzmann theory.
The results we obtained show that, in contrast to the mean-field theory, the
renormalized charge does not saturate, but exhibits a maximum value and then
decays monotonically as the bare charge increases. The results also suggest
that beyond the counterion layer near to the macroion surface, the ionic cloud
is not a diffuse layer which can be handled by means of the linearized theory,
as the two-state model claims, but a more complex structure is settled by the
correlations between microions.
