Fractal geometry of critical Potts clusters

TL;DR

This paper investigates the fractal structure of critical Potts clusters through numerical simulations, analyzing various geometric features and their scaling corrections, highlighting slow convergence to asymptotic behavior.

Contribution

It provides detailed numerical analysis of the fractal geometry of Potts clusters and tests recent correction-to-scaling theories at criticality.

Findings

Data consistent with correction-to-scaling theory

Slow approach to asymptotic scaling

No definitive correction exponents identified

Abstract

Numerical simulations on the total mass, the numbers of bonds on the hull, external perimeter, singly connected bonds and gates into large fjords of the Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at criticality are presented. The data are found consistent with the recently derived corrections-to-scaling theory. However, the approach to the asymptotic region is slow, and the present range of the data does not allow a unique identification of the exact correction exponents