Triangular lattice antiferromagnet — competing interactions and ground state degeneracy
On a triangular lattice with antiferromagnetic J>0, it is impossible to simultaneously satisfy all three bonds on any triangle — this is geometric frustration. The ground state degeneracy is exponential in system size (Wannier 1950: S = 0.3231k_B per spin). Spin ice on pyrochlore lattices extends this to 3D, with 2-in/2-out ice rules and emergent magnetic monopoles as excitations (Castelnovo, Moessner & Sondhi 2008).