Fluctuation-induced, first-order transition in a bcc Ising model with competing interactions

Landau theory predicts that the bcc, spin-½ Ising model with nearest-neighbor ferromagnetic interaction $K_1$ and next-nearest-neighbor antiferromagnetic interaction $K_2$ has a continuous transition with a two-component order parameter ($n=2\mathrm{}$) between the paramagnetic and the type-II antiferromagnetic (A${\mathrm{F}}_2$) phases for $\frac{K_1}{K_2}<\frac{3}{2}$. For $\frac{K_1}{K_2}\lesssim \frac{3}{2}$, we show that this system has a transition temperature, determined from matching high- and low-temperature free-energy series, which is well above the temperature at which the susceptibility diverges. This supports the conclusion, also drawn from renormalization-group and Monte Carlo calculations, that the transition is driven first order by fluctuations. In the deep A${\mathrm{F}}_2$ regime, $\frac{K_1}{K_2}<1.3\mathrm{}$, our series evidence cannot distinguish between a continuous transition and a first-order transition with small discontinuities.