Related papers: The probability distribution of the conductance in…
Scaling of the conductances and the finite-size localization lengths is generalized to anisotropic systems and tested in two dimensional systems. Scaling functions of isotropic systems are recovered once the dimension of the system in each…
Distribution of the conductance P(g) at the critical point of the metal-insulator transition is presented for three and four dimensional orthogonal systems. The form of the distribution is discussed. Dimension dependence of P(g) is proven.…
The probability distribution of the conductance p(g) of disordered 2d and 3d systems is calculated by transfer matrix techniques. As expected, p(g) is Gaussian for extended states while for localized states it is log-normal. We find that at…
The probability distribution of the conductance Pc(g) at the Anderson critical point is calculated. It is find that Pc(g) has a dip at small g in agreement with epsilon expansion results. The Pc(g) for the 3d system is quite different from…
The probability distribution of the conductance at the mobility edge, $p_c(g)$, in different universality classes and dimensions is investigated numerically for a variety of random systems. It is shown that $p_c(g)$ is universal for systems…
Several phenomena related to the critical behaviour of non-interacting electrons in a disordered 2d tight-binding system with a magnetic field are studied. Localization lengths, critical exponents and density of states are computed using…
We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean…
The full distribution of the conductance $P(G)$ in quasi-one-dimensional wires with rough surfaces is analyzed from the diffusive to the localization regime. In the crossover region, where the statistics is dominated by only one or two…
Paper reviews recent numerical data for the conductance distribution of disordered systems in the critical regime and in the localized regime. Of particular interest is the non-analytical form of the critical conductance distribution in the…
Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for…
Scale-invariant universal crossing probabilities are studied for critical anisotropic systems in two dimensions. For weakly anisotropic standard percolation in a rectangular-shaped system, Cardy's exact formula is generalized using a…
We consider two-dimensional system of particles localized on randomly distributed sites of squared lattice with anisotropic transfer matrix elements between localized sites. By summing of "diffusion ladder" and "cooperon ladder" type…
We study numerically the form of the conductance distribution in the non-metallic regime for (1) weakly disordered systems which become insulating due to increase of the system length and (2) cubic d-dimensional systems, in which…
In bootstrap percolation it is known that the critical percolation threshold tends to converge slowly to zero with increasing system size, or, inversely, the critical size diverges fast when the percolation probability goes to zero. To…
The Anderson delocalization-localization transition is studied in multilayered systems with randomly placed interlayer bonds of density $p$ and strength $t$. In the absence of diagonal disorder (W=0), following an appropriate perturbation…
While the tunneling conductance between two spherical-like conducting particles depends on the relative inter-particle distance, the wave function overlap between states of two rod-like particles, and so the tunneling conductance, depends…
The probability distribution of the order parameter is exploited in order to obtain the criticality of magnetic systems. Monte Carlo simulations have been employed by using single spin flip Metropolis algorithm aided by finite-size scaling…
Anisotropic disordered system are studied in this work within the random barrier model. In such systems the transition probabilities in different directions have different probability density functions. The frequency-dependent conductivity…
Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic…
The critical behavior at a corner in two-dimensional Ising and three-state Potts models is studied numerically on the square lattice using transfer operator techniques. The local critical exponents for the magnetization and the energy…