Frustrated Magnets / Spin Ice

Spin ice (Dy₂Ti₂O₇): ferromagnetic Ising spins on pyrochlore lattice. Ice rule: 2-in, 2-out per tetrahedron (maps to Bernal-Fowler ice rules). Pauling entropy: S = Nk_B ln(3/2)/2. Defects (3-in 1-out / 1-in 3-out) are magnetic monopoles, connected by Dirac strings.