Universal amplitude ratios of two-dimensional percolation from field theory

TL;DR

This paper calculates universal amplitude ratios for 2D percolation using a form factor approach, providing a precise estimate for the cluster size ratio that aligns well with numerical lattice results.

Contribution

It advances the theoretical determination of universal amplitude ratios in 2D percolation by completing the two-kink approximation analysis.

Findings

Cluster size ratio estimated at 160.2

Results agree with lattice estimate 162.5 +/- 2

Provides a theoretical value for a previously elusive ratio

Abstract

We complete the determination of the universal amplitude ratios of two-dimensional percolation within the two-kink approximation of the form factor approach. For the cluster size ratio, which has for a long time been elusive both theoretically and numerically, we obtain the value 160.2, in good agreement with the lattice estimate 162.5 +/- 2 of Jensen and Ziff.