Related papers: Rigidity percolation on aperiodic lattices
In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4,6,12) and (3^4,6) lattices using the linearity approximation described in (Scullard and Ziff, J. Stat. Mech. P03021), implemented as a…
Percolation and jamming phenomena are investigated for random sequential deposition of rectangular needles on $d=2$ square lattices. Associated thresholds $p_c^{perc}$ and $p_c^{jam}$ are determined for various needle sizes. Their ratios…
We study the percolation of a quantum particle on quasicrystal lattices and compare it with the square lattice. For our study, we have considered quasicrystal lattices modelled on the pentagonally symmetric Penrose tiling and the…
We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic…
We consider anisotropic independent bond percolation models on the slab $\Z^2\times\{0,\dots,k\}$, where we suppose that the axial (vertical) bonds are open with probability $p$, while the radial (horizontal) bonds are open with probability…
We consider a tiling model of the two-dimensional square-lattice, where each site is tiled with one of the sixteen Wang tiles. The ground states of this model are all quasi-periodic. The systems undergoes a disorder to quasi-periodicity…
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…
An universal invariant for site and bond percolation thresholds (p_{cs} and p_{cb} respectively) is proposed. The invariant writes {p_{cs}}^{1/a_s}{p_{cb}}^{-1/a_b}=\delta/d where a_s, a_b and \delta are positive constants,and d the space…
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…
We investigate percolation, a probabilistic model for continuous phase transition (CPT), on square and weighted planar stochastic lattices. In its thermal counterpart, entropy is minimally low where order parameter (OP) is maximally high…
We consider p-wave (triplet) pairing of single hyperfine state ultracold atomic gases trapped in quasi-two-dimensional optical lattices. We find that the critical temperatures in the lattice model is considerably higher and experimentally…
Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard (inverse) percolation, the lattice is initially…
We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with…
Porous media are often modelled as systems of overlapping obstacles, which leads to the problem of two percolation thresholds in such systems, one for the porous matrix and the other one for the void space. Here we investigate these…
Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on…
The AlPdMn quasicrystal approximants xi, xi', and xi'_n of the 1.6 nm decagonal phase and R, T, and T_n of the 1.2 nm decagonal phase can be viewed as arrangements of cluster columns on two-dimensional tilings. We substitute the tiles by…
The ranges of transmission of the mobiles in a Mobile Ad-hoc Network are not uniform in reality. They are affected by the temperature fluctuation in air, obstruction due to the solid objects, even the humidity difference in the environment,…
Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of…
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…
This short exposition presents an algorithm for an exact calculation of patch frequencies for the rhombic Penrose tiling. We recall a construction of Penrose tilings via dualisation, and by extending the known method for obtaining vertex…