Quantum transport in randomly diluted quantum percolation clusters in two dimensions

We study the hopping transport of a quantum particle through finite, randomly diluted percolation clusters in two dimensions. We investigate how the transmission coefficient T behaves as a function of the energy E of the particle, the occupation concentration p of the disordered cluster, the size of the underlying lattice, and the type of connection chosen between the cluster and the input and output leads. We investigate both the point-to-point contacts and the busbar type of connection. For highly diluted clusters we find the behavior of the transmission to be independent of the type of connection. As the amount of dilution is decreased we find sharp variations in transmission. These variations are the remnants of the resonances at the ordered, zero-dilution, limit. For particles with energies within 0.25≤E≤1.75 (relative to the hopping integral) and with underlying square lattices of size 20×20, the configurations begin transmitting near p_α=0.60 with T against p curves following a common pattern as the amount of dilution is decreased. Near p_β=0.90 this pattern is broken and the transmission begins to vary with the energy. In the asymptotic limit of very large clusters we find the systems to be totally reflecting in almost all cases. A few clear exceptions we find are when the amount of dilution is very low, when the particle has energy close to a resonance value at the ordered limit, and when the particle has energy at the middle of the band. These three cases, however, may not exhaust all possible exceptions.     

Test of scaling in two dimensions

The purpose of this paper is to report on the first comprehensive experimental test of the scaling hypothesis in two-dimensional physics. This hypothesis predicts that the equation of state near a phase transition of a system in thermodynamic equilibrium obeys a simple scaling law. Our experimental data, obtained on a truly two-dimensional magnetic system consisting of a subnanometer thick Fe films grown on top of a non-magnetic surface, explicitly display scaling. The experimental evidence suggests that this system is an almost perfect realization of a 2d Ising model.     

Plaquette percolation on frustrated lattices in two dimensions

We study the ±J quenched-random-bond Ising model in two dimensions. Critical concentrations for percolation of frustrated and normal plaquettes are calculated for the triangular and square lattices by computer simulation. Connection with T = 0 statistical properties is discussed.     

Finite size scaling approach to a metamagnetic model in two dimensions

We investigate the tricritical properties of a metamagnetic model, namely the next-nearest neighbor Ising antiferromagnet, in two dimensions. We calculate the transfermatrix on finite strips and use finite size scaling to obtain the critical line. The tricritical point and its exponents are obtained by two different methods. In the case of strong intersublattice coupling no evidence for tricritical behavior is found.     

Invasion percolation between two sites in two, three, and four dimensions

The mass distribution of invaded clusters in non-trapping invasion percolation between an injection site and an extraction site has been studied, in two, three, and four dimensions. This study is an extension of the recent study focused on two dimensions by Araújo et al. [A.D. Araújo, T.F. Vasconcelos, A.A. Moreira, L.S. Lucena, J.S. Andrade Jr., Phys. Rev. E 72 (2005) 041404] with respect to higher dimensions. The mass distribution exhibits a power-law behavior, P(m)∝m^−α. It has been found that the index α for p_e<p_c, p_c being the percolation threshold of a regular percolation, appears to be independent of the value of p_e and is also independent of the lattice dimensionality. When p_e=p_c, α appears to depend marginally on the lattice dimensionality, and the relation α=τ−1, τ being the exponent associated with cluster size distribution of a regular percolation via n_s∝s^−τ, appears to be valid.     

Metal-insulator transition in two dimensions: experimental test of the two-parameter scaling

We report a detailed scaling analysis of resistivity rho(T,n) measured for several high-mobility 2D electron systems in the vicinity of the 2D metal-insulator transition. We analyzed the data using the two-parameter scaling approach and general scaling ideas. This enables us to determine the critical electron density, two critical indices, and temperature dependence for the separatrix in the self-consistent manner. In addition, we reconstruct the empirical scaling function describing a two-parameter surface which fits well the rho(T,n) data.     

Bond percolation in two and three dimensions: Numerical evaluation of time-dependent transport properties

For random walks on two- and three-dimensional cubic lattices, numerical results are obtained for the static,D(), and time-dependent diffusion coefficientD(t), as well as for the velocity autocorrelation function (VACF). The results cover all times and include linear and quadratic terms in the density expansions. Within the context of kinetic theory this is the only model in two and three dimensions for which the time-dependent transport properties have been calculated explicitly, including the long-time tails.     

Infinite clusters in percolation models

The qualitative nature of infinite clusters in percolation models is investigated. The results, which apply to both independent and correlated percolation in any dimension, concern the number and density of infinite clusters, the size of their external surface, the value of their (total) surface-to-volume ratio, and the fluctuations in their density. In particular it is shown thatN ₀, the number of distinct infinite clusters, is either 0, 1, or and the caseN ₀= (which might occur in sufficiently high dimension) is analyzed.Alfred P. Sloan Research Fellow, Research supported in part by National Science Foundation grant No. MCS 77-20683 and by the U.S.-Israel Binational Science Foundation.Research supported in part by the U.S.Israel Binational Science Foundation.     

Monte Carlo study of percolation of random discs in two dimensions: Variable range interaction

Monte Carlo study of percolation of random discs in two dimensions with variable range of interaction is carried out. The critical exponents β and γ are found to be the same when analysed as a function of range of interaction or critical area fraction, for all levels of dilution.     

Monte Carlo study of phase diagram for correlated site-bond percolation in two dimensions

At the critical point of the square Ising model, the percolation threshold for randomly active bonds between up spins is close top _Bc =0.60 and seems compatible with the predictionp _Bc =1-exp(–2J/k _B T _c )=0.586 of Coniglio and Klein. Longer simulations on larger lattices are necessary for a more precise clarification.     

Corrections to cluster-radius scaling for branched polymers and percolation

We report analyses of series enumerations for the mean radius of gyration for isotropic and directed lattice animals and for percolation clusters, in two and three dimensions. We allow for the leading correction to the scaling behaviour and obtain estimates of the leading correction-to-scaling exponent . We find -0.640±0.004 and =0.87±0.07 for isotropic animals in 2d, and =0.64±0.06 in 3d. For directed lattice animals we argue that the leading correction has= or= ; we also estimate =0.82±0.01 and 0.69 ±0.01 ind=2, 3 respectively. For percolation clusters at and abovep _c, we find (p _c) =0.58±0.06 and (p>p _c)=0.84±0.09 in 2d, and (p _c)=0.42±0.11 and (p>p _c)=0.41 ±0.09 in 3d.     

随机多孔介质逾渗模型渗透率的临界标度性质

研究了一类非零键渗透率满足均匀分布的随机多孔介质逾渗模型-数值计算了该模型系统渗透率在临界点处的标度指数-结果表明该指数并不能看作是普适常数,而与均匀分布的参数有关-这意味着即使非零键渗透率值的概率密度函数满足负一阶矩存在条件,系统渗透率在逾渗临界点处的标度指数仍然依赖于分布函数的具体参数,并不是常数-这一数值结果与Sahimi对此问题的结论不同- 关键词： 逾渗 随机多孔介质 标度指数 渗透率     

Nonequilibrium second-order phase transitions in stochastic lattice systems: A finite-size scaling analysis in two dimensions

Two-dimensional lattice-gas models with attractive interactions and particleconserving happing dynamics under the influence of a very large external electric field along a principal axis are studied in the case of a critical density. A finite-size scaling analysis allows the evaluation of critical indexes for the infinite system asβ=0.230±0.003,v=0.55±0.2, and α 0. We also describe some qualitative features of the system evolution and the existence of certain anisotropic order even well above the critical temperature in the case of finite lattices.