Eur. Phys. J. B 34, 479-487 (2003)
https://doi.org/10.1140/epjb/e2003-00247-7

Fractal geometry of critical Potts clusters

¹ Helsinki Institute of Physics and Laboratory of Physics, Helsinki University of Technology, Finland
² Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
³ Department of Mathematics, Yale University, New Haven, CT 06520-8283, USA

Corresponding author: ^a joonas.asikainen@inf.ethz.ch

Received: 4 December 2002
Revised: 2 June 2003
Published online: 9 September 2003

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. A new method for thermalization of spin systems is presented. The method allows a speed up of an order of magnetization for large lattices. We also show snapshots of the Potts clusters for different values of q, which clearly illustrate the fact that the clusters become more compact as q increases, and that this affects the fractal dimensions in a monotonic way. 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.