Series expansion study of the percolation probability for the triangular lattice bond problem

Abstract

The percolation probability P(p) defined as the probability that a given lattice site belongs to an infinite cluster is expanded in powers of q(=1-p), the probability of a missing bond, to order 31 on the triangular lattice. The series is used to estimate the critical exponent beta . The results are compared with those obtained from P(p), the probability that a given lattice bond belongs to an infinite cluster. It is concluded that the estimate of the common critical exponent beta of these functions is greater than to be expected from either series separately and find beta =0.139+or-0.003.