Percolation and Magnetization in the Continuous Spin Ising Model

In the strong coupling limit the partition function of SU(2) gauge theory can be reduced to that of the continuous spin Ising model with nearest neighbour pair-interactions. The random cluster representation of the continuous spin Ising model in two dimensions is derived through a Fortuin-Kasteleyn transformation, and the properties of the corresponding cluster distribution are analyzed. It is shown that for this model, the magnetic transition is equivalent to the percolation transition of Fortuin-Kasteleyn clusters, using local bond weights. These results are also illustrated by means of numerical simulations.