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We obtain the phase diagram of the hard core lattice gas with third nearestneighbor exclusion on the triangular lattice using Monte Carlo simulations thatare 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 thirdnearest neighbor exclusion undergoes two phase transitions with increasingdensity, with the phase at intermediate densities exhibiting hexatic order withcontinuously varying exponents. Though a hexatic phase is expected when theexclusion range is large, it has not been seen earlier in hard core latticegases with short range exclusion. In this paper, by numerically determining theentropies for all densities, we show unambiguously that there is only a singlephase transition in the system between a low-density fluid phase and ahigh-density ordered sublattice phase, and that a hexatic phase is absent. Thetransition is shown to be first order in nature and the critical parameters aredetermined accurately.

Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: one or two phase transitions?