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 ($\sqrt{3}\times \sqrt{3}$) phases (one with $\frac{1}{3}$ of the sites occupied and one with $\frac{2}{3}$ 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 $\mathrm{XY}$-like line of critical points which exist between upper and lower temperatures $T_1$ and $T_2$, respectively. Along this line between $T_1$ and $T_2$ we find nonuniversal critical behavior and identify topological (vortexlike) excitations.