The effects of discretization on geometric frustration;a study of a Potts-like spin lattice system.

Geometric frustration arises whenever the geometry and/or the topology of the space a system is embedded in forbids the motifs locally favored by the constituents’ interactions, from being propagated. Geometric frustration arises naturally in a range of systems and displays a variety of responses from local resolution of the frustration to complex highly cooperative ground states with super extensive energy. A recent work focusing on frustration in continuous systems allowed predicting the energy exponent of frustrated systems from studying their compatibility conditions. However, systems with discrete DOF show dramatically different behavior.

In this work we study an N-state Potts spin-lattice system in which frustration is induced by favoring a slight misalignment between adjacent spins. The response ranges from being trivial and non-cumulative to cooperative and complex, depending on N. In the limit of N→ ∞, the super extensive ground state obtained for bent-core liquid crystals, which inspired this model, is recovered. The discretization of the DOF along with the compatibility conditions gives rise to topological-like features and coupling between response modes. These features are observed in numerical simulations and explained theoretically.