Scaling relations for 2 D-percolation

Abstract

We prove that the relations 2 D-percolation hold for the usual critical exponents for 2 D-percolation, provided the exponents δ and v exist. Even without the last assumption various relations (inequalities) are obtained for the singular behavior near the critical point of the correlation length, the percolation probability, and the average cluster size. We show that in our models the above critical exponents have the same value for approach of p to the critical probability from above and from below. © 1987 Springer-Verlag.