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

Abstract

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 $H=J\Sigma {\mathrm{nn}}^{}{\sigma }_i{\sigma }_j-\alpha J\Sigma {\mathrm{nnn}}^{}{\sigma }_i{\sigma }_j$, ${\sigma }_i=\pm 1$, $J>\mathrm{}0\mathrm{}$. 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 $-1\mathrm{}\lesssim \alpha \lesssim 0.25$. For larger values of $\left|\alpha \right|$ 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 $\alpha$ at which it has been applied, namely, 0 and -0.25. For $\alpha \lesssim -0.5\mathrm{}$ renormalization-group arguments strongly indicate that the transition is first order. If this is so, then our results indicate that the discontinuities for $\alpha <-1\mathrm{}$ must be very small. The nature of the ground states changes at $\alpha =0\mathrm{} \mathrm{and} -0.5\mathrm{}$. At these values of $\alpha$ the ground states are infinitely degenerate. The structure of the low-temperature phases, at all values of $\alpha$, is discussed.