Visualize self-consistent mean-field solutions for the Ising model. The equation m=tanh(βJzm+βh) solved graphically. Watch bifurcations as temperature crosses Tc=Jz.
Mean-field Ising: m = tanh(Jz·m/T + h/T). Graphical solution: intersections of y=m and y=tanh(βJzm+βh). Below Tc=Jz: slope βJz>1 → three solutions (one unstable). Exact for fully-connected (Curie-Weiss) model. Critical exponents: β=1/2, δ=3, γ=1 — mean-field universality class, exact for d≥4.