Universal amplitude ratios in the two-dimensional $q$-state Potts model and percolation from quantum field theory

TL;DR

This paper uses quantum field theory to compute universal amplitude ratios in the 2D q-state Potts model and percolation, providing new precise predictions and confirming known results.

Contribution

It applies the form factor approach to the Potts model, deriving universal amplitude ratios and extending results to the percolation limit q→1.

Findings

Good agreement with exact results for amplitude ratios

Predicted a ratio close to 74 for percolation cluster sizes

Extended form factor methods to the q→1 percolation limit

Abstract

We consider the scaling limit of the two-dimensional $q$-state Potts model for $q\leq 4$. We use the exact scattering theory proposed by Chim and Zamolodchikov to determine the one and two-kink form factors of the energy, order and disorder operators in the model. Correlation functions and universal combinations of critical amplitudes are then computed within the two-kink approximation in the form factor approach. Very good agreement is found whenever comparison with exact results is possible. We finally consider the limit $q\to 1$ which is related to the isotropic percolation problem. Although this case presents a serious technical difficulty, we predict a value close to 74 for the ratio of the mean cluster size amplitudes above and below the percolation threshold. Previous estimates for this quantity range from 14 to 220.