What you are watching. Each cell is a tiny magnet (spin) that points up or down. Neighbouring spins prefer to align — but thermal agitation tries to scramble them. The Metropolis Monte Carlo rule flips a random spin with probability min(1, e^{−ΔE / k_BT}). Below the critical temperature T_c = 2 / ln(1 + √2) ≈ 2.269 (Onsager, 1944) the lattice spontaneously magnetises into large aligned domains — a true second-order phase transition. Right at T_c domains appear at every scale (critical opalescence) and the susceptibility diverges. Above T_c the spins are a disordered paramagnet. Drag the temperature slider slowly across 2.269 to feel the transition.