Correlation function of four spins in the percolation model

TL;DR

This paper calculates the four-spin correlation function in the percolation limit of the Potts model using Coulomb gas techniques, revealing new fusion channels related to specific operator dimensions.

Contribution

It introduces a Coulomb gas method to compute four-spin correlations in percolation, uncovering new fusion channels in the model.

Findings

Fusion of two spins yields a new channel with dimension 5/8.

Four-point functions define the fusion rules of the model.

The method provides explicit correlation functions in the percolation limit.

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 $\Delta=5/8$.