2D Ising Model — Correlation Length

The 2D Ising model has an exact phase transition at T_c = 2/ln(1+√2) ≈ 2.269 (in units of J/k_B). Near T_c, the spin-spin correlation length ξ diverges as ξ ~ |T−T_c|^{-ν} with ν = 1. Watch domains grow and measure the correlation length.

Temperature T: 2.27

T_c = 2.269 | T/T_c = 1.00 | ξ ≈ — | ⟨m⟩ = —

Left: spin lattice (white=+1, dark=−1). Right: normalized correlation C(r) = ⟨s(0)s(r)⟩ — fit gives ξ.