  Geometric frustration results from a discrepancy between the locally favored
arrangement of the constituents of a system and the geometry of the embedding
space. Geometric frustration can be either non-cumulative, which implies an
extensive energy growth, or cumulative which implies super-extensive energy
scaling and highly cooperative ground state configurations which may depend on
the dimensions of the system. Cumulative geometric frustration was identified
in a variety of continuous systems including liquid crystals, filament bundles
and molecular crystals. However, a spin-lattice model which clearly
demonstrates cumulative geometric frustration was lacking. In this work we
describe a non-linear variation of the XY-spin model on a triangular lattice
that displays cumulative geometric frustration. The model is studied
numerically and analyzed in three distinct parameter regimes, which are
associated with different energy minimizing configurations. We show that,
despite the difference in the ground state structure in the different regimes,
in all cases the super-extensive power-law growth of the frustration energy for
small domains grows with the same universal exponent that is predicted from the
structure of the underlying compatibility condition.
