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 t13 and the form factor behaves as k for small k then must be 4. Experimental and numerical results give 4.