Metropolis algorithm on 100×100 lattice. Each spin s_i ∈ {±1} flips with P = min(1, e^{−ΔE/kT}), ΔE = 2s_i Σ_j s_j. Critical temperature T_c = 2J/(k ln(1+√2)) ≈ 2.269. Below T_c: long-range order and spontaneous magnetization. Above: disordered paramagnetic phase.