title: Conductivity of Coniglio-Klein clusters.
abstract: We performed numerical simulations of the q-state Potts model to compute the reduced conductivity exponent t/ν for the critical Coniglio-Klein clusters in two dimensions, for values of q in the range [1,4]. At criticality, at least for q<4, the conductivity scales as C(L) ~ L(-t/ν), where t and ν are, respectively, the conductivity and correlation length exponents. For q=1, 2, 3, and 4, we followed two independent procedures to estimate t/ν. First, we computed directly the conductivity at criticality and obtained t/ν from the size dependence. Second, using the relation between conductivity and transport properties, we obtained t/ν from the diffusion of a random walk on the backbone of the cluster. From both methods, we estimated t/ν to be 0.986 ± 0.012, 0.877 ± 0.014, 0.785 ± 0.015, and 0.658 ± 0.030, for q=1, 2, 3, and 4, respectively. We also evaluated t/ν for noninteger values of q and propose the conjecture 40 gt/ν = 72 + 20 g - 3g(2) for the dependence of the reduced conductivity exponent on q, in the range 0 ≤ q ≤ 4, where g is the Coulomb gas coupling.
authors.affiliation: Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstrasse 6, CH-8093 Zurich, Switzerland. posen@ifb.baug.ethz.ch
authors.forename: Nicolas
authors.initials: N
authors.lastname: Posé
authors.forename: N A M
authors.initials: NA
authors.lastname: Araújo
authors.forename: H J
authors.initials: HJ
authors.lastname: Herrmann
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D004553:Electric Conductivity; D008956:Models, Chemical; D008958:Models, Molecular; D010316:Particle Size; D011789:Quantum Theory
chemical_list: D003102:Colloids