Correlation function of four spins in the percolation model

Abstract

By using the Coulomb gas technics we calculate the four-spin correlation function in the percolation $q\rightarrow 1$ limit of the Potts model. It is known that the four-point functions define the actual fusion rules of a particular model. In this respect, we find that fusion of two spins, of dimension $\Delta_{\sigma}=\frac{5}{96}$, produce a new channel, in the 4-point function, which is due to the operator with dimension $\Delta=5/8$.