title: Fractality of largest clusters and the percolation transition in power-law diluted chains.
abstract: Relying on the fractal character of the largest clusters at criticality, we employ a finite-size scaling analysis to obtain an accurate phase-diagram of the percolation transition in chains with bond concentration decaying as a power-law on the form 1/ r(1+sigma) . For the particular case of sigma=1, no percolation transition is observed to occur at a finite dilution, in contrast with the finite temperature Kosterlitz-Thouless transition exhibited in Ising and Potts chains with inverse square-law couplings. The fractal dimension of the critical percolation cluster is found to follow distinct dependencies on the decay exponent being numerically fitted by d(f) =0.35+4sigma/5 for 0<sigma<1/2 and d(f) = (1+sigma) /2 for 1/2<sigma<1 . We also compute average mass ratios of the two largest clusters at criticality.
authors.affiliation: Departamento de Física, Universidade Federal de Alagoas, Maceió-AL, 57072-970, Brazil.
authors.forename: S S
authors.initials: SS
authors.lastname: Albuquerque
authors.forename: F A B F
authors.initials: FA
authors.lastname: de Moura
authors.forename: M L
authors.initials: ML
authors.lastname: Lyra
authors.forename: A J F
authors.initials: AJ
authors.lastname: de Souza