0 Percolation and Magnetization for Generalized Continuous Spin Models

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 continuous spin Ising model. We show on the basis of numerical simulations that such an equivalence can be generalized to a wider class of theories, including spin distribution functions, longer range interactions and self-interaction terms.