Four spins correlation function of the $q$ states Potts model, for general values of $q$. Its percolation model limit $q \rightarrow 1$

TL;DR

This paper derives a general formula for the four-spin correlation function in the $q$-state Potts model for any $q$ between 1 and 4, including the percolation limit as $q$ approaches 1.

Contribution

It provides a unified expression for four-spin correlations in the Potts model for all $q$ in [1,4], including the percolation case, based on conformal field theory assumptions.

Findings

Derived the four-spin correlation function for general $q$ in the Potts model.

Analyzed the $q ightarrow 1$ limit to obtain results for percolation.

Connected conformal field theory operators with spin correlations.

Abstract

Under the assumption that the product of two spin operators decomposes uniquely into the degenerate conformal fields $\{\Phi_{n',n}\}$, the general expression for the correlation function of four spins is defined for the $q$ states Potts model with $q$ taking general values in the interval $1 \leq q \leq 4$. The limit of $q \rightarrow 1$ is considered in detail and the four spins function is obtained for the percolation model.