Correlation-length exponent in two-dimensional percolation and Potts model

Abstract

Following Reynolds et al. and Swendsen, Monte Carlo renormalization calculations were made for percolation on the triangular lattice for rescaling up to 10000×10000, and for the 4-state Potts model on square lattices up to 64×64. In contrast to earlier studies, our comparison with the den Nijs hypothesis gives good agreement with its prediction $y=\frac{3}{4}$ for percolation but bad agreement with its prediction $y=\frac{3}{2}$ for the 4-state Potts model.