Conductivity of Coniglio-Klein clusters
| Autor: | Pose, Nicolas, Araujo, Nuno A. M., Herrmann, Hans J. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 86, 051140 (2012) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.86.051140 |
| Popis: | 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 values of $q$ in the range $[1;4]$. At criticality, at least for $q<4$, the conductivity scales as $C(L) \sim L^{-\frac{t}{\nu}}$, where $t$ and $\nu$ are, respectively, the conductivity and correlation length exponents. 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 also evaluated $t /\nu$ for non integer values of $q$ and 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. Comment: 10 figures and 2 tables |
| Databáze: | arXiv |
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