Spin Ice & Frustrated Magnets

Ice rules, magnetic monopoles, and Dirac strings

Controls

Ice rule: 2-in, 2-out per vertex
Ice rule violations: 0
Monopole pairs: 0
MC sweeps: 0
Energy/spin:
Spin ice: Ising spins on each bond of a square ice lattice, constrained by the "2-in, 2-out" ice rule at every vertex (analogous to Bernal-Fowler water ice rules). Violations create pairs of magnetic monopoles connected by a Dirac string of flipped spins. At low T, ice-rule states dominate — the ground state is massively degenerate (Pauling entropy). Increasing T excites monopole pairs.