1207.3930 (Nicolas Pose et al.)

Conductivity of Coniglio-Klein clusters    [PDF]

Nicolas Pose, Nuno A. M. Araujo, Hans J. Herrmann

We performed numerical simulations of the $q$-state Potts model to compute the reduced conductivity exponent $t/ \nu$ for the critical Coniglio-Klein clusters in two dimensions. For $q=1$, 2, 3, and 4, we followed two independent procedures to estimate $t / \nu$. First, we computed directly the conductivity at criticality and obtained $t / \nu$ from the size dependence. Second, using the relation between conductivity and transport properties, we obtained $t / \nu$ from the diffusion of a random walk on the backbone of the cluster. From both methods, we estimated $t / \nu$ to be $0.986 \pm 0.012$, $0.877 \pm 0.014$, $0.785 \pm 0.015$, and $0.658 \pm 0.030$, for $q=1$, 2, 3, and 4, respectively. We propose the following conjecture $40gt/ \nu=72+20g-3g^2$ for the dependence of the reduced conductivity exponent on $q$, in the range $ 0 \leq q \leq 4$, where $g$ is the Coulomb gas coupling.

View original: http://arxiv.org/abs/1207.3930