  We analyze the percolation properties of certain clusters defined on
configurations of the 2--dimensional Heisenberg model. We find that, given any
direction \vec{n} in O(3) space, the spins almost perpendicular to \vec{n} form
a percolating cluster. This result gives indications of how the model can avoid
a previously conjectured Kosterlitz-Thouless phase transition at finite
temperature T.
