  For the Ising model, the spin magnetization transition is equivalent to the
percolation transition of Fortuin-Kasteleyn clusters; this result remains valid
also for the conventional continuous spin Ising model. The investigation of
more general continuous spin models may help to obtain a percolation
formulation for the critical behaviour in SU(2) gauge theory. We therefore
study a broad class of theories, introducing spin distribution functions,
longer range interactions and self-interaction terms. The thermal behaviour of
each model turns out to be in the Ising universality class. The corresponding
percolation formulations are then obtained by extending the Fortuin-Kasteleyn
cluster definition; in several cases they illustrate recent rigorous results.
