Percolation and magnetization in the continuous spin Ising model

In the strong coupling limit the partition function of SU(2) gauge theory c an be reduced to that of the continuous spin Ising model with nearest neigh bour 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 distributio n are analyzed. It is shown that for this model, the magnetic transition is equivalent to the percolation transition of Fortuin-Kasteleyn clusters, us ing local bond weights. These results are also illustrated by means of nume rical simulations. (C) 2000 Elsevier Science B.V. All rights reserved.