Non-trivial attenuation of geometric frustration by discretization of the degrees of freedom: A study of a Potts-like frustrated spin system

Abstract

The resolution of geometric frustration in systems with continuous degrees of freedom (DOF) often involves long-range cooperative response and super-extensive energy scaling. In contrast, frustrated Ising-like spin systems show only a local and uniform resolution of the frustration. In this work we bridge between these two extremes by studying a frustrated N -state Potts-like spin model and varying N . The expected cooperative response, observed for large N , is strongly attenuated as N is reduced. Moderate N values show unique phases that result from the discrete compatibility conditions.