  We prove that by scaling nearest-neighbour ferromagnetic energies defined on
Poisson random sets in the plane we obtain an isotropic perimeter energy with a
surface tension characterised by an asymptotic formula. The result relies on
proving that cells with `very long' or `very short' edges of the corresponding
Voronoi tessellation can be neglected. In this way we may apply Geometry
Measure Theory tools to define a compact convergence, and a characterisation of
metric properties of clusters of Voronoi cells using limit theorems for
subadditive processes.
