H = −J Σ_{⟨ij⟩} s_i s_j − h Σ_i s_i
The 2D Ising model was solved exactly by Lars Onsager (1944) — the first rigorous proof of a phase transition. At Tc = 2J/ln(1+√2) ≈ 2.269J, the system undergoes a second-order transition. All models in the
2D Ising universality class share the same critical exponents regardless of microscopic details. The exponents β=1/8, γ=7/4, ν=1 are exact and non-mean-field — a triumph of the renormalization group framework. The order parameter (magnetization) vanishes as |T-Tc|^β near Tc.