2D Ising Model at Criticality

Lars Onsager solved the 2D Ising model exactly in 1944 — one of the triumphs of mathematical physics. The critical temperature T_c = 2J/ln(1+√2) separates ordered (M≠0) from disordered phases. At T_c: correlation length ξ → ∞, susceptibility diverges as |t|^(-7/4), and spin clusters are self-similar fractals with dimension d_f = 91/48 (same as percolation!). The order parameter vanishes as M ~ |t|^β with β = 1/8.