Monte Carlo studies of an fcc Ising antiferromagnet with nearest- and next-nearest-neighbor interactions

We have investigated, via Monte Carlo computations, the phase diagram of an ordering binary alloy-equivalent to an Ising spin system-on an fcc lattice with nearest- and next-nearest-neighbor pair interactions $H=J{Σ}{nn}^{}{{σ}}ᵢ{{σ}}ⱼ{-}{α}J{Σ}{nnn}^{}{{σ}}ᵢ{{σ}}ⱼ$, ${{σ}}ᵢ=±{}1$, $J>0$. Our studies indicate that this system undergoes a first-order transition; i.e., there is a discontinuity in the energy and order parameters as a function of temperature, for values ${-}1{}{α}{}0.25$. For larger values of $|{α}|$ the transition appears to be continuous, without any metastable states. Our results are in good agreement with Kikucki's cluster variation method at the two values of ${α}$ at which it has been applied, namely, 0 and -0.25. For ${α}{}{-}0.5$ renormalization-group arguments strongly indicate that the transition is first order. If this is so, then our results indicate that the discontinuities for ${α}<{-}1$ must be very small. The nature of the ground states changes at ${α}=0 and {-}0.5$. At these values of ${α}$ the ground states are infinitely degenerate. The structure of the low-temperature phases, at all values of ${α}$, is discussed.