Ground states of the Ising model at fixed magnetization on a triangular ladder with three-spin interactions

We study the Ising model at fixed magnetization on a triangular ladder with three-spin interactions. By recasting the ground-state determination as a linear programming (LP) problem, we solve it exactly using standard LP techniques. We construct the phase diagram for arbitrary fixed magnetization and identify three types of ground states: periodic, phase-separated, and ordered but aperiodic. When magnetization is treated as a free parameter, the ground state adopts only periodic configurations with the average magnetization per site $0$, $\pm 1\mathrm{/}3$ or $\pm 1$, except for the phase boundaries.