LOGARITHMIC CORRECTIONS FOR THE PERCOLATIVE PROPERTIES OF THE 4-STATE POTTS-MODEL

Abstract

Clusters in the Potts model are connected sets of nearest neighbour sites for which the spin variables are in the same state. Droplets can be obtained by adding bonds with probability p = 1 - exp(-K) between the sites in a cluster (where K is the Potts model's inverse temperature). When q-->4, renormalization group (RG) fixed points describing clusters and droplets will coalesce, leading to logarithmic corrections. We calculate the precise form of these corrections used in a differential RG method. Our predictions are then tested using extensive Monte Carlo calculations. Theory and the simulations are found to be in excellent agreement.