  We have considered two classical lattice-gas models, consisting of particles
that carry multicomponent magnetic momenta, and associated with a
two-dimensional square lattices; each site can host one particle at most, thus
implicitly allowing for hard-core repulsion; the pair interaction, restricted
to nearest neighbors, is ferromagnetic and involves only two components. The
case of zero chemical potential has been investigated by Grand--Canonical Monte
Carlo simulations; the fluctuating occupation numbers now give rise to
additional fluid-like observables in comparison with the usual
saturated--lattice situation; these were investigated and their possible
influence on the critical behaviour was discussed. Our results show that the
present model supports a Berezinskii-Kosterlitz-Thouless phase transition with
a transition temperature lower than that of the saturated lattice counterpart
due to the presence of ``vacancies''; comparisons were also made with similar
models studied in the literature.
