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We performed numerical simulations of the $q$-state Potts model to compute the reduced conductivity exponent $t/ u$ 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 $C(L) sim L^{-frac{t}{ u}}$, where $t$ and $ u$ are, respectively, the conductivity and correlation length exponents. For q=1, 2, 3, and 4, we followed two independent procedures to estimate $t / u$. First, we computed directly the conductivity at criticality and obtained $t / u$ from the size dependence. Second, using the relation between conductivity and transport properties, we obtained $t / u$ from the diffusion of a random walk on the backbone of the cluster. From both methods, we estimated $t / u$ 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 $t / u$ for non integer values of $q$ and propose the following conjecture $40gt/ u=72+20g-3g^2$ 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.
The emergence of scanning probe and electron beam imaging techniques have allowed quantitative studies of atomic structure and minute details of electronic and vibrational structure on the level of individual atomic units. These microscopic descripto
Using a recently developed thermodynamic integration method, we compute the precise values of the excess Gibbs free energy (G^e) of the high density liquid (HDL) phase with respect to the crystalline phase at different temperatures (T) in the superco
We extend our 2+1 dimensional discrete growth model (PRE 79, 021125 (2009)) with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence. By mapping
Lattice dynamical methods used to predict phase transformations in crystals typically deal with harmonic phonon spectra and are therefore not applicable in important situations where one of the competing crystal structures is unstable in the harmonic
The main purpose of this work is to simulate two-phase flow in the form of immiscible displacement through anisotropic, three-dimensional (3D) discrete fracture networks (DFN). The considered DFNs are artificially generated, based on a general distri