Related papers: Percolation in the canonical ensemble
We comment on the nature of the ordering transition of a model of equilibrium polydisperse rigid rods, on the square lattice, which is reported by Lopez et al. to exhibit random percolation criticality in the canonical ensemble, in sharp…
In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree…
We study the critical behavior of the $d=3$ Ising model with bond randomness through extensive Monte Carlo simulations and finite-size scaling techniques. Our results indicate that the critical behavior of the random-bond model is governed…
We generate point configurations (PCs) by thresholding the local energy of the Ashkin-Teller model in two dimensions (2D) and study the percolation transition at different values of $\lambda$ along the critical Baxter line by varying the…
In this article, we revisit random site and bond percolation in square lattice focusing primarily on the behavior of entropy and order parameter. In the case of traditional site percolation, we find that both the quantities are zero at…
We consider uniform random permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons. The limit depends on the generating series of the simple permutations in the class. Under a mild…
When addressing the thermodynamics of finite-sized systems, one must specify whether one wants to fix conserved charges to a sharp value or whether one is content to fix their thermodynamic average. In other words, contrary to the…
We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result the growth process involves a diverging…
We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a post-selection inference approach to canonical correlation analysis. The challenge is to adjust for the selection…
In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $\alpha>0$ is fixed and $\beta \geq 0$ is a parameter. As $d$ and $\alpha$ vary, the model…
The Canonical Transformation theory of Yanai and Chan [J. Chem. Phys. 124, 194106 (2006)] provides a rigorously size-extensive description of dynamical correlation in multireference problems. Here we describe a new formulation of the theory…
The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied for the first time to a model suffering the notorious quantum Monte Carlo sign problem --- the orbital $e_g$…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
A region of two-dimensional space has been filled randomly with large number of growing circular discs allowing only a `slight' overlapping among them just before their growth stop. More specifically, each disc grows from a nucleation…
We prove that for Bernoulli percolation on $\mathbb{Z}^d$, $d\geq 2$, the percolation density is an analytic function of the parameter in the supercritical interval. For this we introduce some techniques that have further implications. In…
The counterion-condensation transition at charged cylinders is studied using Monte-Carlo simulation methods. Employing logarithmically rescaled radial coordinates, large system sizes are tractable and the critical behavior is determined by…
We present high statistics simulations for 2-d percolation clusters in the "bus bar" geometry at the critical point, for site and for bond percolation. We measured their backbone sizes and electrical conductivities. For all sets of…
Canonical transformations are defined and discussed along with the exponential, the coherent and the ultracoherent vectors. It is shown that the single-mode and the $n$-mode squeezing operators are elements of the group of canonical…
Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel…
The aim of the paper is to present numerical results supporting the presence of conformal invariance in three dimensional statistical mechanics models at criticality and to elucidate the geometric aspects of universality. As a case study we…