Phase transitions in an Ising model for monolayers of coadsorbed atoms

A Monte Carlo method is used to study a simple $S=1$ Ising (lattice-gas) model appropriate for monolayers composed of two kinds of atoms on cubic metal substrates $H={K}ₙₙ{Σ}{nn}^{}{S}iz²{S}jz²+{J}ₙₙₙ{Σ}{nnn}^{}{S}iz{S}jz+{Δ}{Σ}{i}^{}{S}iz²$ (where nn denotes nearest-neighbor and nnn next-nearest-neighbor pairs). The phase diagram is determined over a wide range of ${Δ}$ and $T$ for ${{K}ₙₙ}{{J}ₙₙₙ}=1/4$. For small (or negative) ${Δ}$ we find an antiferromagnetic 2×{}1 ordered phase separated from the disordered state by a line of second-order phase transitions. The 2×{}1 phase is separated by a line of first-order transitions from a c(2×2) phase which appears for larger Δ. The 2×{}1 and c(2×2) phases become simultaneously critical at a bicritical point and the phase boundary of the c(2×2){→}disordered transition shows a tricritical point.