Scaling relation for the critical exponents of the backbone of percolation clusters

Abstract

The author suggests that beta _B, the critical exponent of the backbone of percolation clusters, is given by beta _B=¹/₂( gamma +5 beta )-1, where gamma and beta are susceptibility and order parameter exponents of percolation respectively. The proposed relation agrees with the epsilon expansion of beta _B given by Harris and Lubensky and provides accurate estimates of beta _B at all d>1. This relation may suggest that the backbone exponents are not independent of other percolation exponents. The author also suggests a more general relation for the order parameter exponent of m-connected clusters.