1D Ising Model — Exact Transfer Matrix Solution

The transfer matrix T = [[e^(K+h), e^(-K)], [e^(-K), e^(K-h)]] diagonalizes the 1D Ising partition function exactly. All thermodynamic quantities follow from eigenvalues λ±. No phase transition at finite T (in 1D).

Temperature T (J/kB): 2.0

Coupling J: 1.0

Field h (J): 0.0

Chain length N: 40

Transfer matrix T = ...

λ+ (max eigenvalue)—

λ- (min eigenvalue)—

Free energy f/J—

Magnetization ⟨m⟩—

Susceptibility χ—

Corr. length ξ—