  The Ising model at inverse temperature $\beta$ and zero external field can be
obtained via the Fortuin-Kasteleyn (FK) random-cluster model with $q=2$ and
density of open edges $p=1-e^{-\beta}$ by assigning spin +1 or -1 to each
vertex in such a way that (1) all the vertices in the same FK cluster get the
same spin and (2) +1 and -1 have equal probability. We generalize the above
procedure by assigning spin +1 with probability $r$ and -1 with probability
$1-r$, with $r \in [0,1]$, while keeping condition (1). For fixed $\beta$, this
generates a dependent (spin) percolation model with parameter $r$. We show
that, on the triangular lattice and for $\beta<\beta_c$, this model has a
percolation phase transition at $r=1/2$, corresponding to the Ising model. This
sheds some light on the conjecture that the high temperature Ising model on the
triangular lattice is in the percolation universality class and that its
scaling limit can be described in terms of SLE$_6$. We also prove uniqueness of
the infinite +1 cluster for $r>1/2$, sharpness of the percolation phase
transition (by showing exponential decay of the cluster size distribution for
$r<1/2$), and continuity of the percolation function for all $r \in [0,1]$.
