Odd-spin-cluster interactions

We consider interactions of Ising spins three at a time, five at a time, etc., as distinguished from the conventional interactions (two at a time). To illustrate, we calculate the exact thermodynamics of three-spin-cluster interactions in one dimension with and without a magnetic field. We find regular structures except at a certain value of the coupling constant ratio ($\frac{J_1}{J_3}=-3\mathrm{}$) where the ground state becomes chaotic. The $T\to 0$ limit of the magnetization agrees with the exact ground-state calculation.