LATTICE SHAPES AND SCALING FUNCTIONS FOR BOND RANDOM PERCOLATION ON HONEYCOMB LATTICES

We use a histogram Monte Carlo simulation method to calculate the scal ing functions of the existence probability E(p) and the percolation pr obability P of the bond random percolation model on honeycomb lattices with aspect ratios of 0.5 and 2.0. We find that such different aspect ratios give quite different scaling functions near the critical regio n. However, they give a consistent critical point, critical exponents, and the thermodynamic order parameter from renormalization-group calc ulations. Some interesting theoretical problems related to this work a re discussed.