We consider a variational problem on the d-dimensional lattice Z(d) wh
ich has applications in the study of the metastable behavior of the st
ochastic Ising model. The problem, an isoperimetric one, is to iind wh
at is the smallest area a finite subset of Z(d) can have restricted to
three classes of subsets of Z(d). If phi is one of these subsets, we
define its volume as the number of points in it and its area as the nu
mber of pairs of points in Z(d) which are neighbors and such that only
one of them belongs to phi.