  In this paper we studythe asymptotics of singularly perturbed
phase-transition functionals of the form \[ F_k(u)=\frac{1}{\epsilon_k}\int_A
f_k(x,u,\epsilon_k\nabla u)\,dx\,, \]
  where $u \in [0,1]$ is a phase-field variable, $\epsilon_k>0$ a
singular-perturbation parameter, i.e., $\epsilon_k \to 0$, as $k\to +\infty$,
and the integrands $f_k$ are such that, for every $x$ and every $k$,
$f_k(x,\cdot ,0)$ is a double well potential with zeros at 0 and 1. We prove
that the functionals $F_k$ $\Gamma$-converge (up to subsequences) to a surface
functional of the form \[ F_\infty(u)=\int_{S_u\cap
A}f_\infty(x,\nu_u)\,d\mathcal H^{n-1}\,,\] where $u\in BV(A;\{0,1\})$ and
$f_\infty$ is characterised by the double limit of suitably scaled minimisation
problems. Afterwards we extend our analysis to the setting of stochastic
homogenisation and prove a $\Gamma$-convergence result for stationary random
integrands.
