  We study the large scale equilibrium behavior of Van der Waals-Cahn-Hilliard
phase transitions in stationary ergodic media. Specifically, we are interested
in free energy functionals of the following form \begin{equation*}
\mathcal{F}^{\omega}(u) = \int_{\mathbb{R}^{d}} \left(\frac{1}{2}
\varphi^{\omega}(x,Du(x))^{2} + W(u(x)) \right) \, dx, \end{equation*} where
$W$ is a double-well potential and $\varphi^{\omega}(x,\cdot)$ is a stationary
ergodic Finsler metric. We show that, at large scales, the random energy
$\mathcal{F}^{\omega}$ can be approximated by the anisotropic perimeter
associated with a deterministic Finsler norm $\tilde{\varphi}$. To find
$\tilde{\varphi}$, we build on existing work of Alberti, Bellettini, and
Presutti, showing, in particular, that there is a natural sub-additive quantity
in this context.
