We have considered a classical lattice-gas model, consisting of a two-dimensional lattice $Z^2$, each site of which hosts at most one two-component unit vector; particles occupying pairs of nearest-neighbouring sites interact via the ferromagnetic potential
\benl
\Psi_{jk}= -\epsilon \nu_j \nu_k \Omega_{jk}, ~\Omega_{jk}={\bg u}_j \cdot {\bg u}_k,
\eenl
where $\nu_j=0,1$ denotes occupation numbers, ${\bg u}_j$ are the unit vectors (classical spins), and $\epsilon$ is a positive constant setting energy and temperature scales; the total Hamiltonian is given by
\benl
\lambda =W/\epsilon=-\sum_{\{ j < k \}} (\nu_j \nu_k) \Omega_{jk} -\mu N,~N= \sum_k \nu_k,
\eenl
where $\sum_{\{j < k\}}$ denotes sum over all distinct nearest-neighbouring pairs of lattice sites. The saturated-lattice version of this model, where all sites are occupied, supports the well-known Berezhinskii-Kosterlitz-Thouless transition; we report here a simulation study, carried out for both $\mu= 0.1$ and $\mu=-0.2$, showing evidence of a transition of this kind, in broad qualitative agreement with previous Renormalization-Group studies.

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