1D Ising — Exact Transfer Matrix

The 1D Ising model is exactly solvable via the transfer matrix T:

T = [[e^(J+h), e^(−J)], [e^(−J), e^(J−h)]]

Z = Tr(Tᴺ) = λ₊ᴺ + λ₋ᴺ. Correlation length ξ = −1/ln(λ₋/λ₊). In 1D, no phase transition for T>0 — spins are disordered. The correlation length diverges only at T→0.