Metropolis MC simulation · Tc = 2/ln(1+√2) ≈ 2.269 J/kB
Spin lattice (↑ white, ↓ black)
Lars Onsager (1944) solved the 2D Ising model exactly: the free energy has a logarithmic singularity at Tc. The spontaneous magnetization is M = (1 − sinh(2J/kT)⁻⁴)^(1/8) for T < Tc. The plot shows measured |M| (blue dots) vs the exact Onsager curve (gold) and marks Tc.