H = J Σ_{⟨ij⟩} σᵢσⱼ, J > 0
On triangle: 3 bonds, only
2 can be satisfied → frustration
S_residual = Nk·ln(W)/N
W ≈ (4/3)^{3N/2} (Wannier 1950)
Energy/N: —
|Magnetization|: —
Frustrated bonds: —
On a triangular lattice, antiferromagnetic (J>0) interactions are geometrically frustrated:
you cannot color all 3 corners of a triangle with opposing spins. This creates a massive
ground-state degeneracy (Wannier entropy S/N·k = 0.3231) — no long-range order at T→0.
Compare to square lattice where frustration is absent.