Universality and Scaling for the Structure Factor in Dynamic Order-Disorder Transitions

TL;DR

This paper demonstrates that the average scattering intensity during order-disorder transitions exhibits a universal form, largely independent of local free-energy details, and confirms theoretical predictions through numerical simulations.

Contribution

It provides numerical evidence supporting the universality of the structure factor in order-disorder transitions and compares these results with existing theoretical models.

Findings

Numerical integration confirms universality across different free-energy forms.

The structure factor matches Ohta-Jasnow-Kawasaki theory except near cross-over regions.

Results support the inclusion of a wide range of local free-energy forms in the Model A class.

Abstract

The universal form for the average scattering intensity from systems undergoing order-disorder transitions is found by numerical integration of the Langevin dynamics. The result is nearly identical for simulations involving two different forms of the local contribution to the free energy, supporting the idea that the Model A dynamical universality class includes a wide range of local free-energy forms. An absolute comparison with no adjustable parameters is made to the forms predicted by the theories of Ohta-Jasnow-Kawasaki and Mazenko. The numerical results are well described by the former theory, except in the cross-over region between scattering dominated by domain geometry and scattering determined by Porod's law.