Geometric frustration prevents long-range order — degenerate ground states
On a triangular lattice with antiferromagnetic coupling, no spin arrangement can simultaneously satisfy all bonds — at least one triangle must have two spins aligned. This is geometric frustration.
Unlike square lattices, the AFM triangular Ising model has no unique ground state. There is a macroscopic degeneracy ∝ 1.2^N ground states (Wannier 1950), giving residual entropy at T=0.
Colors: up (↑) / down (↓). Red bonds = frustrated.