Scaling and the Small-Wave-Vector Limit of the Form Factor in Phase-Ordering Dynamics

The consequences of the scaling hypothesis in phase-ordering dynamics are examined. Dynamics governed by the time-dependent Ginzburg-Landau and Cahn-Hilliard-Cook equations are studied. An upper bound is found for the dynamical exponents. It is also found that for a critical quench with Cahn-Hilliard-Cook dynamics, if the length scale of the patterns increases as $t^{\frac{1}{3}}$ and the form factor behaves as $k^{\delta }$ for small $k$ then $\delta$ must be ≥ 4. Experimental and numerical results give $\delta \simeq 4$.