Frustrated Magnetism: Kagome Antiferromagnet

Kagome Lattice: Corner-sharing triangles with coordination z=4. The key frustration: with antiferromagnetic J>0, no spin arrangement satisfies all triangle bonds simultaneously — every triangle has at least one frustrated pair.

Macroscopic Degeneracy: The ground state has extensive entropy S ∝ N (Pauling-like), scaling as 2^(N/9). The low-energy manifold satisfies only the "ice rule" analog: each triangle has net zero spin.

Flat Band: The tight-binding Hamiltonian on kagome has a completely flat band (dispersionless) — localized eigenstates exist due to destructive interference. This promotes quantum spin liquid behavior.

Colors: Red=spin↑, Blue=spin↓. Frustrated bonds shown in yellow. Spin-1/2 Ising model on kagome lattice.