Critical and multicritical behavior in a triangular-lattice-gas Ising model: Repulsive nearest-neighbor and attractive next-nearest-neighbor coupling

Monte Carlo simulations have been used to study a triangular lattice-gas (Ising) model with repulsive nearest-neighbor interactions and attractive next-nearest-neighbor coupling. We find two ordered (√3×√3) phases (one with 1/3 of the sites occupied and one with 2/3 of the sites filled). These ordered phases are separated from the disordered state by a phase boundary which is second order at high temperatures and which has tricritical points and first-order transitions at low temperatures. The critical and tricritical exponents are consistent with those predicted for the three-state Potts model. At 50% coverage we find a low-temperature ordered phase which is separated from the disordered state by an XY-like line of critical points which exist between upper and lower temperatures T₁ and T₂, respectively. Along this line between T₁ and T₂ we find nonuniversal critical behavior and identify topological (vortexlike) excitations.