  We study the thermodynamic and structural properties of a simple, one-patch
fluid model using the reference hypernetted-chain (RHNC) integral equation and
specialized Monte Carlo simulations. In this model, the interacting particles
are hard spheres, each of which carries a single identical,
arbitrarily-oriented, attractive circular patch on its surface; two spheres
attract via a simple square-well potential only if the two patches on the
spheres face each other within a specific angular range dictated by the size of
the patch. For a ratio of attractive to repulsive surface of 0.8, we construct
the RHNC fluid-fluid separation curve and compare with that obtained by Gibbs
ensemble and grand canonical Monte Carlo simulations. We find that RHNC
provides a quick and highly reliable estimate for the position of the
fluid-fluid critical line. In addition, it gives a detailed (though
approximate) description of all structural properties and their dependence on
patch size.
