  The critical behaviour of the Ising model in the absence of an external
magnetic field can be specified either through spontaneous symmetry breaking
(thermal criticality) or through cluster percolation (geometric criticality).
We extend this to finite external fields for the case of the Potts' model,
showing that a geometric analysis leads to the same first order/second order
structure as found in thermodynamic studies. We calculate the Kert\'esz line,
separating percolating and non-percolating regimes, both analytically and
numerically for the Potts model in presence of an external magnetic field.
