  The generalized Lin-Taylor model defined on the hexagonal lattice is used to
investigate the phase separation in an asymmetric binary liquid mixture
consisting of large A (hexagons) and small B (triangles) particles. By
considering interaction energies between A-A and A-B pairs of particles that
occupy nearest-neighbour cells of the hexagonal lattice, we have derived an
exact solution for the considered model system having established a mapping
correspondence with the two-dimensional Ising model on its dual triangular
lattice. Altogether, six different types of coexistence curves including those
with reentrant miscibility regions (i.e. closed-loop coexistence curves) were
found in dependence on the relative strength between both coupling constants.
