In kagome spin ice, Ising spins on corner-sharing triangles obey the ice rules (2-in, 1-out or 1-in, 2-out per triangle), leading to a macroscopic ground state degeneracy and extensive residual entropy S₀ = (3/2)k_B ln(4/3).
Ice rules: Each triangle must satisfy: exactly 2 spins pointing in, 1 out (or 1 in, 2 out). Analogous to the Bernal-Fowler ice rules for proton disorder in water ice. Violations create emergent magnetic monopoles (spin ice defects). The kagome lattice has 3-coordinated vertices; the residual entropy S₀ = (3/2)Nk_B ln(4/3) per spin was calculated by Wills, Ballou & Lacroix (2002). Blue arrows = inward (into triangle center), red = outward; pink triangles = ice-rule violations (monopoles).