Fractal dimensions and corrections to scaling for critical Potts clusters

TL;DR

This paper uses renormalization group and Coulomb gas methods to derive theoretical predictions for corrections to the scaling behavior of critical Potts clusters, including logarithmic corrections at q=4.

Contribution

It provides new theoretical predictions for corrections to the fractal masses of Potts clusters, including exact logarithmic corrections for q=4.

Findings

Predicted corrections to fractal masses of clusters.

Derived exact logarithmic corrections for q=4.

Enhanced understanding of scaling corrections in Potts models.

Abstract

Renormalization group and Coulomb gas mappings are used to derive theoretical predictions for the corrections to the exactly known asymptotic fractal masses of the hull, external perimeter, singly connected bonds and total mass of the Fortuin-Kasteleyn clusters for two-dimensional $q$-state Potts models at criticality. For q=4 these include exact logarithmic (as well as loglog) corrections.