Critical Exponents & Data Collapse

10, 20, 40, 80, 160
Collapse quality: adjust β and ν to align curves
Near a continuous phase transition, observables obey finite-size scaling: M(T,L) = L−β/ν f[(T−T_c)L1/ν]. Plotting raw data gives five different curves (left). Using the correct critical exponents β and ν, rescaling collapses all curves onto a single universal function (right). This "data collapse" is how physicists extract exponents from simulations. The collapse quality score rewards how tightly the rescaled curves align — find the Ising 2D exponents β=1/8, ν=1 to see perfect collapse!