Disordered charge distributions and dielectric loss in extra dense flint glasses

The complex permittivities of some extra dense flint glasses (EDF glasses) have been studied. The dielectric features of the samples are dominated by their PbO content. Both refractive indices and dielectric losses exhibit a close relation to the concentration of Pb ions. The latter are located either at sites of the network atoms or filling the potential minima interstitially. They can be identified by their different relaxation mechanisms. The dispersion in the submillimeter wave and FIR area is characterized by a very broad distribution of comparably sharp resonant states. Thermal lens — or hysteresis effects can be excluded.     

Knoten und quadratische Formen

Ohne Zusammenfassung     

Rapidly converging asymptotic expansions in ± J Ising lattices

Ground-state properties of Ising lattices with different concentrations of ±J interactions are studied analytically. Rapidly converging expansions are obtained for the average frustration segment, energy per bond, and fraction of the lattice without frustration. Triangular, square and honeycomb lattices are considered. Physical properties are calculated by means of two independent theoretical methods. Numerical simulations are also carried out for sets of samples in each topology. The agreement between analytic expressions and numerical simulations is quite good in the method of the star. Such agreement improves for the method of the sublattice. Both methods are also in very good agreement with previous extensive calculations performed for the particular case of equal concentration of ±J interactions.     

Site–bond percolation on triangular lattices: Monte Carlo simulation and analytical approach

A generalization of the pure site and pure bond percolation problems called site–bond percolation on a triangular lattice is studied. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S∩B$S\cap B$ and S∪B$S\cup B$) for site–bond percolation are used. In S∩B$S\cap B$ (S∪B$S\cup B$), two points are said to be connected if a sequence of occupied sites and (or  ) bonds joins them. By using finite-size scaling theory, data from S∩B$S\cap B$ and S∪B$S\cup B$ are analyzed in order to determine (i$i$) the phase boundary between the percolating and non-percolating regions and (ii$ii$) the numerical values of the critical exponents of the phase transition occurring in the system. A theoretical approach, based on exact calculations of configurations on finite triangular cells, is applied to study the site–bond percolation on triangular lattices. The percolation processes have been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied elements. A comparison of the results obtained by these two methods has been performed and discussed.     

Local analysis of frustration based on Kagomé lattices

Magnetic frustration in the framework of the Edwards-Anderson model is studied for the ground level (T=0) of the Kagomé lattice (KL). A sample consists of a realization of a random distribution of ferromagnetic (F) and antiferromagnetic (AF) interactions of the same strength along lines connecting nearest neighbors. Our goal is to compare two methods to calculate the following parameters: ground state energy, frustration and average frustration segment as functions of x, the concentration of F bonds. In doing so we make use of topological concepts such as plaquettes and frustration segments. The probability of a plaquette being unfrustrated (or flat) is ℘_p(x), while the probability of a plaquette being frustrated (or curved) is ℘_c(x). The analysis is done locally on a representative portion of the lattice which is called cell; cells of two different sizes are used in the present work. One method (which is simpler) is based on the probability function of any plaquette configuration ?(℘_p,℘_c). The other method is more exact but also more complex and increasingly difficult to use for large cells; it is based on the probability of bond configurations ψ(x). These methods are compared between themselves noting that the simpler method can be enough for most of the range for x. In addition, numerical simulations for many random samples at different concentrations x for a size given by 75 spins with periodic boundary conditions were done. This provides reference lines to compare with the properties under study. The local frustration analysis to obtain both ?(℘_p,℘_c) and ψ(x) is done over two cells of different size. Robustness of the criteria used in the local frustration analysis is also investigated.