  We compute the form factors of the order and disorder operators, together
with those of the stress-energy tensor, of the two-dimensional three-state
Potts model with vacancies along its thermal deformation of the critical point.
At criticality the model is described by the non-diagonal partition function of
the unitary minimal model $\mathcal{M}_{6,7}$ of conformal field theories and
is accompanied by an internal $S_3$ symmetry. Its off-critical thermal
deformation is an integrable massive theory which is still invariant under
$S_3$. The presence of infinitely many conserved quantities, whose spin
spectrum is related to the exceptional Lie algebra $E_6$, allows us to
determine the analytic $S$-matrix, the exact mass spectrum and the matrix
elements of local operators of this model in an exact non-perturbative way. We
use the spectral representation series of the correlators and the fast
convergence of these series to compute several universal ratios of the
renormalization group.
