Giambattista Giacomin and Joel L. Lebowitz
Exact Macroscopic Description of Phase Segregation in Model Alloys
with Long Range Interactions
(26K, AmsTeX)
ABSTRACT. We derive an exact nonlinear non-local macroscopic equation for the time
evolution of the conserved order parameter $\rho({\text{\bf r}}, t)$ of a
microscopic model binary
alloy undergoing phase segregation: a $d$--dimensional
lattice gas
evolving via Kawasaki exchange dynamics, satisfying
detailed balance for a Hamiltonian with a long range pair potential
$\gamma^d J(\gamma \vert
x \vert)$.
The
macroscopic evolution is on the spatial scale
$\gamma^{-1}$ and time scale $\gamma^{-2}$, in the
limit $\gamma \to 0$. The domain coarsening, described by
interface motion, is
similar to that obtained from the Cahn-Hilliard equation.
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Pacs numbers: 05.20.-y, 02.30Jr, 02.50Cw, 64.75+g, 64.70.Kb