Phase Ordering Kinetics — Coarsening
Allen-Cahn (t^{1/2}) and Cahn-Hilliard (t^{1/3}) domain growth laws
After a quench below T_c, the order parameter φ phase-separates and coarsens.
Allen-Cahn (Model A): ∂φ/∂t = −δF/δφ = φ − φ³ + κ∇²φ. Domain size L(t) ~ t^{1/2}.
Cahn-Hilliard (Model B): ∂φ/∂t = ∇²(δF/δφ). Conserved dynamics → L(t) ~ t^{1/3} (Lifshitz-Slyozov).
The slower exponent reflects the diffusive transport required to conserve mass.
Log-log plot shows measured L(t) vs the theoretical power law.