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.
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