Freezing phase transition in hard-core lattice gases on the triangular lattice with exclusion up to seventh next-nearest neighbor.

Hard-core lattice-gas models are minimal models to study entropy-driven phase transitions. In the k-nearest-neighbor lattice gas, a particle excludes all sites up to the kth next-nearest neighbors from being occupied by another particle. As k increases from one, it extrapolates from nearest-neighbor exclusion to the hard-sphere gas. In this paper we study the model on the triangular lattice for k≤7 using a flat histogram algorithm that includes cluster moves. Earlier studies focused on k≤3. We show that for 4≤k≤7, the system undergoes a single phase transition from a low-density fluid phase to a high-density sublattice-ordered phase. Using partition function zeros and nonconvexity properties of the entropy, we show that the transitions are discontinuous. The critical chemical potential, coexistence densities, and critical pressure are determined accurately.