Bridging cumulative and noncumulative geometric frustration response via a frustrated N -state spin system

The resolution of geometric frustration in systems with continuous degrees of freedom often involves a cooperative inhomogeneous response and superextensive energy scaling. In contrast, the frustration in frustrated Ising-like spin systems is resolved uniformly. In this work we bridge between these two extremes by studying a frustrated model composed of N-state spins, and varying N. The expected cooperative response, observed for large N, is strongly attenuated as N is reduced, in a nontrivial way. Moderate N values show unique topological-like phases not observed before in frustrated models.