Ising Transfer Matrix

Exact solution of the 1D Ising model via transfer matrix. Compute free energy, magnetization, and correlation length exactly. Visualize the 2×2 transfer matrix eigenvalues and thermodynamic quantities.

Transfer matrix T for 1D Ising: T_{σ,σ'} = exp(Kσσ' + h(σ+σ')/2). Free energy f = -kT ln(λ₊). Correlation length ξ = -1/ln(λ₋/λ₊). The 1D model has no phase transition at T>0 (Ising 1925). In 2D, Onsager (1944) solved via a 2^L × 2^L transfer matrix — the first exact phase transition calculation in statistical mechanics.