  We obtain the phase diagram of the hard core lattice gas with third nearest
neighbor exclusion on the triangular lattice using Monte Carlo simulations that
are based on a rejection-free flat histogram algorithm. In a recent paper [J.
Chem. Phys. 151, 104702 (2019)], it was claimed that the lattice gas with third
nearest neighbor exclusion undergoes two phase transitions with increasing
density, with the phase at intermediate densities exhibiting hexatic order with
continuously varying exponents. Though a hexatic phase is expected when the
exclusion range is large, it has not been seen earlier in hard core lattice
gases with short range exclusion. In this paper, by numerically determining the
entropies for all densities, we show unambiguously that there is only a single
phase transition in the system between a low-density fluid phase and a
high-density ordered sublattice phase, and that a hexatic phase is absent. The
transition is shown to be first order in nature and the critical parameters are
determined accurately.
