Equality of the Bond Percolation Critical Exponents for Two Pairs of Dual Lattices

Abstract

The substitution method is used to show that the percolative behaviour of the triangular and hexagonal lattices bond percolation models are similar near their critical probabilities. As a consequence, if the limits defining the critical exponents β and γ exist, these lattices have the same values of β and γ. Similarly, the method also shows equality of the β and γ values for bond percolation models on the bowtie lattice and its dual.