Clusters and Ising critical droplets: a renormalisation group approach

Abstract

The Migdal-Kadanoff renormalisation group for two-dimensions is employed to obtain the global phase diagram for the site-bond correlated percolation problem. It is found that the Ising critical point (K=Kc,H=O) is a percolation point for a range of bond probability rho B such that 1>or= rho B>or=1-e-2Kc. In particular, as rho B approaches 1-e-2Kc, the percolation clusters become less compact and coincide with the Ising critical droplets.