  The clusters of up spins of a two-dimensional Ising ferromagnet undergo a
second order percolative transition at temperatures above the Curie point. We
show that in the scaling limit the percolation threshold is described by an
integrable field theory and identify the non-perturbative mechanism which
allows the percolative transition in absence of thermodynamic singularities.
The analysis is extended to the Kertesz line along which the Coniglio-Klein
droplets percolate in a positive magnetic field.
