Phase separation in asymmetric binary mixture of large hexagonal and small rhombus particles described within the generalised Frenkel-Louis model

The generalised Frenkel-Louis model, which is defined for asymmetric binary mixture of large hexagonal and small rhombus particles on a hexagonal lattice, is exactly solved by establishing a rigorous mapping equivalence with the one-component lattice-gas model and the corresponding spin-1/2 Ising model on a triangular lattice. This precise approach enables one to investigate in detail how the phase separation and critical behaviour in a close vicinity of demixing depends on pressure and inter-particle interactions. The binary mixture with the attractive inter-particle interaction exhibits diverse coexistence curves including asymmetric liquid-vapour coexistence curves, symmetric or asymmetric liquid-liquid coexistence curves, while asymmetric liquid-liquid coexistence curves always occur in the binary system with the repulsive inter-particle interaction.