Related papers: Duality with real-space renormalization and its ap…
We consider a percolation process in which $k$ points separated by a distance proportional to system size $L$ simultaneously connect together ($k>1$), or a single point at the center of a system connects to the boundary ($k=1$), through…
The star-triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular and hexagonal lattices. Among the consequences are box-crossing (RSW)…
The results of investigations of main characteristics of a one-dimensional percolation theory (percolation threshold, critical exponents of correlation radius and specific heat, and free energy) are presented for the problem of bonds and…
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
Zhang found a simple, elegant argument deducing the non-existence of an infinite open cluster in certain lattice percolation models (for example, p=1/2 bond percolation on the square lattice) from general results on the uniqueness of an…
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)],…
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…
We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory, and determine the level spacing distributions, which, with…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
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 show analytically that the $[0,1]$, $[1,1]$ and $[2,1]$ Pad{\'e} approximants of the mean cluster number $S(p)$ for site and bond percolation on general $d$-dimensional lattices are upper bounds on this quantity in any Euclidean…
We revisit the problem of Stone duality for lattices with various quasioperators, first studied in [14], presenting a fresh duality result. The new result is an improvement over that of [14] in two important respects. First, the…
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
The permutation model is a classical spin system where elements of the symmetric group interact with one another. The partition function of this model is directly related to the entanglement structure of random quantum circuits and random…
We study the one-dimensional contact process in its quantum version using a recently proposed real space renormalisation technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply…
We study site- and bond-percolation on a class of lattices referred to as Lieb lattices. In two dimensions the Lieb lattice (LL) is also known as the decorated square lattice, or as the CuO$_2$ lattice; in three dimensions it can be…
The analytical study of confinement in lattice gauge theories (LGTs) remains a difficult task to this day. Taking a geometric perspective on confinement, we develop a real-space renormalization group (RG) formalism for $\mathbb{Z}_2$ LGTs…
We consider independent and $m$-dependent two-dimensional oriented site percolation with open-site density close to one started from Bernoulli product measures. We show that the probability of an occupied interval in the former process…
We report on the exact treatment of a random-matrix representation of bond percolation model on a square lattice in two dimensions with occupation probability $p$. The percolation problem is mapped onto a random complex matrix composed of…
Recently, Scullard and Ziff noticed that a broad class of planar percolation models are self-dual under a simple condition that, in a parametrized version of such a model, reduces to a single equation. They state that the solution of the…