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

TL;DR

This paper explores how geometric frustration responses transition from cooperative and inhomogeneous in continuous systems to uniform in Ising-like spins by studying an N-state spin model, revealing new phases and attenuation effects.

Contribution

It introduces a unified model of N-state spins that bridges the gap between continuous and discrete frustration responses, uncovering novel topological phases and response behaviors.

Findings

Large N exhibits cooperative inhomogeneous response

Reduced N attenuates the cooperative response in a non-trivial manner

Moderate N reveals unique topological-like phases

Abstract

The resolution of geometric frustration in systems with continuous degrees of freedom often involves a cooperative inhomogeneous response and super-extensive 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 non-trivial way. Moderate N values show unique topological-like phases not observed before in frustrated models.