  In this paper we describe the asymptotic behavior of rigid spin lattice
energies by exhibiting a continuous interfacial limit energy as scaling to zero
the lattice spacing. The limit is not trivial below a percolation threshold: it
can be characterized by two phases separated by an interface. The macroscopic
surface tension at this interface is defined through a first-passage
percolation formula, related to the chemical distance on the square lattice. We
also show a continuity result, that is the homogenization of rigid spin system
is a limit case of the elliptic random homogenization.
