Abstract: I will talk about an old paper of Alexander, Chayes and Chayes on the construction of the "Wulff crystal" for percolation on Z^2: we take p>p_c and condition on the event that the origin is in a large, but finite, cluster. What does the cluster look like? It turns out that there is a limit shape, which is not rotationally invariant, and whose definition involves a notion of surface tension.
I will (try to) explain some ideas related to this paper.