  We study the surface tension and the phenomenon of phase coexistence for the
Ising model on $\mathbbm{Z}^d$ ($d \geqslant 2$) with ferromagnetic but random
couplings. We prove the convergence in probability (with respect to random
couplings) of surface tension and analyze its large deviations : upper
deviations occur at volume order while lower deviations occur at surface order.
We study the asymptotics of surface tension at low temperatures and relate the
quenched value $\tau^q$ of surface tension to maximal flows (first passage
times if $d = 2$). For a broad class of distributions of the couplings we show
that the inequality $\tau^a \leqslant \tau^q$ -- where $\tau^a$ is the surface
tension under the averaged Gibbs measure -- is strict at low temperatures. We
also describe the phenomenon of phase coexistence in the dilute Ising model and
discuss some of the consequences of the media randomness. All of our results
hold as well for the dilute Potts and random cluster models.
