Frustrated Magnet — Kagome Ising

Geometric frustration — extensive ground-state degeneracy, no ordering
E/N: —
|m|: —
H = -J Σ_{⟨ij⟩} s_i s_j
Kagome: corner-sharing triangles. AF Ising is maximally frustrated — no way to satisfy all bonds simultaneously. Residual entropy S₀ ≈ 0.502 k_B per spin (Kano-Naya 1953).
Kagome Frustration: The kagome lattice consists of corner-sharing triangles. For antiferromagnetic (J<0) Ising spins, the constraint that each triangle satisfy all three bonds is impossible — at least one bond is "frustrated." This leads to an extensively degenerate ground state (exponentially many ground states, not just a few). The residual entropy per spin S₀/k_B ≈ 0.502 survives to T→0, violating the third law of thermodynamics for this purely classical model. No long-range magnetic order occurs at any finite temperature. Adding further-neighbor interactions J₂ can lift the degeneracy and drive ordering (order-by-disorder).