Related papers: Honeycomb Lattices with Defects
We investigate how the spectral and topological properties of electron systems evolve on a lattice that interpolates between the honeycomb and its 1/6-depleted structures through the introduction of selective random defects. We find that in…
We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome and diced…
We study random coloring of the hexagons of a honeycomb lattice into $2^{n-1}$ colors (that is the standard Potts model at infinite temperature). It may be considered as a generalization of percolation to $n$ pairwise independent, but…
We investigate site and bond percolation in triangular and square lattices subjected to linear distortion. In contrast to previously studied distortion schemes that preserve lattice geometry, linear distortion dislocates regular lattice…
We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, \textbf{87} 052107 (2013)],…
Natural and artificial honeycomb lattices are of great interest because the band structure of these lattices, if properly constructed, contains a Dirac point. Such lattices occur naturally in the form of graphene and carbon nanotubes. They…
This article presents a Monte Carlo study on bond percolation in distorted square and triangular lattices. The distorted lattices are generated by dislocating the sites from their regular positions. The amount and direction of the…
We study the effects of bond disorder on triangular and honeycomb lattices where each spring has a probability p to be odd elastic. Using an effective medium theory and numerical simulations, we uncover the behavior of odd moduli in the…
In this article, we study a bond percolation model on a horizontally stretched square lattice, constructed by stretching the distances between the columns of $\mathbb{Z}_+^2$ according to a collection of independent and identically…
Covering a graph or a lattice with non-overlapping dimers is a problem that has received considerable interest in areas such as discrete mathematics, statistical physics, chemistry and materials science. Yet, the problem of percolation on…
We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…
We investigate the effect of structural distortion on bond percolation in simple cubic and body-centered cubic lattices using extensive Monte Carlo simulations. Distortion is introduced through controlled random displacements of lattice…
We present a study of radiation propagation through disordered amplifying honeycomb photonic lattice, where elastic scattering provides feedback for light generation. To explore the interplay of different scattering mechanisms and the…
We introduce a bond percolation procedure on a $D$-dimensional lattice where two neighbouring sites are connected by $N$ channels, each operated by valves at both ends. Out of a total of $N$, randomly chosen $n$ valves are open at every…
We use numerical simulations and an effective-medium theory to study the rigidity percolation transition of the honeycomb and diamond lattices when weak bond-bending forces are included. We use a rotationally invariant bond-bending…
Mixed-wet percolation was introduced recently in the context of two-phase flow in porous media. In this model, the sites of the primal lattice are occupied with a certain probability $p$, and bonds are placed on the dual lattice between two…
We present a rough estimation -- up to four significant digits, based on the scaling hypothesis and the probability of belonging to the largest cluster vs. the occupation probability -- of the critical occupation probabilities for the…
We study random bubble lattices which can be produced by processes such as first order phase transitions, and derive characteristics that are important for understanding the percolation of distinct varieties of bubbles. The results are…
The site percolation problem is studied on d-dimensional generalisations of the Kagome' lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d dimensions, namely q=2d. The site…
We present a study of site and bond percolation on periodic lattices with (on average) fewer than three nearest neighbors per site. We have studied this issue in two contexts: By simulating oxides with a mixture of 2-coordinated and…