Conductivity of Coniglio-Klein clusters

Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051140. doi: 10.1103/PhysRevE.86.051140. Epub 2012 Nov 30.

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Colloids / chemistry*
  • Computer Simulation
  • Electric Conductivity
  • Models, Chemical*
  • Models, Molecular*
  • Particle Size
  • Quantum Theory*

Substances

  • Colloids