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Using Monte Carlo simulation, Van Duijneveldt and Lekkerkerker [Phys. Rev. Lett. 71, 4264 (1993)] found gas-liquid-solid behavior in a simple two-dimensional lattice model with two types of hard particles. The same model is studied here by means of numerical transfer-matrix calculations, focusing on the finite-size scaling of the gaps between the largest few eigenvalues. No evidence for a gas-liquid transition is found. We discuss the relation of the model with a solvable restricted solid-on-solid model of which the states obey the same exclusion rules. Finally, a detailed analysis of the relation with the dilute three-state Potts model strongly supports the tricritical point rather than a three-phase point.

Evidence against a three-phase point in a binary hard-core lattice model