Orderings on Lattices and the Interfaces between the Domains that Form

John Cahn
National Institute for Standards and Technology

Gradient systems (large scale ODE) on simple mean field energy functions, constructed to model the behavior chemical species (or scalar spins) on lattices, can reproduce a multitude of ordering phenomena that are observed; a variety of orderings specific to each lattice or lattice complex, and the energies and motions of interfaces between various domains of ordering. These interfaces are anisotropic and show propagation failure at low driving force. Continuizing the discrete lattice formulations to obtain related energy functionals and much-studied PDE retains many of the phenomena, but eliminates the propagation failure and alters the anisotropy.