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

Abstract

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 ${k}^{\ensuremath{\delta}}$ for small $k$ then $\ensuremath{\delta}$ must be \ensuremath{\ge} 4. Experimental and numerical results give $\ensuremath{\delta}\ensuremath{\simeq}4$.