Geometric Frustration — Kagome/Pyrochlore Spin Ice

Spin ice on a kagome lattice: Ising spins on corner-sharing triangles satisfy "2-in/1-out or 1-in/2-out" ice rules (analogous to water ice proton disorder). Geometric frustration prevents long-range order even at T→0 — a residual Pauling entropy S₀ = (1/2)ln(3/2) per site persists. Monte Carlo dynamics with Metropolis sampling.

Energy/site: —
Magnetization: —
Frustrated triangles: —
Green = frustrated (violated ice rule)
Blue ↑ / Red ↓ spins
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