  The critical surface for random-cluster model with cluster-weight $q\ge 4$ on
isoradial graphs is identified using parafermionic observables. Correlations
are also shown to decay exponentially fast in the subcritical regime. While
this result is restricted to random-cluster models with $q\ge 4$, it extends
the recent theorem of the two first authors to a large class of planar graphs.
In particular, the anisotropic random-cluster model on the square lattice is
shown to be critical if $\frac{p_vp_h}{(1-p_v)(1-p_h)}=q$, where $p_v$ and
$p_h$ denote the horizontal and vertical edge-weights respectively. We also
mention consequences for Potts models.
