Related papers: Finite size scaling in three-dimensional bootstrap…
The culling process in Bootstrap Percolation is Abelian since the final stable configuration does not depend on the details of the updating procedure. An efficient algorithm is devised using this idea for the determination of the bootstrap…
Let $ \mathbb{L}^{d} = ( \mathbb{Z}^{d},\mathbb{E}^{d} ) $ be the $ d $-dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on $ \mathbb{L}^{d} $ in which every edge inside the $ s $-dimensional…
Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of…
We calculate numerically universal finite-size-scaling functions for the three-dimensional O(4) and O(2) models. The approach of these functions to the infinite-volume scaling functions is studied in detail on the critical and…
The low energy spectrum of a spin chain with $OSp(3|2)$ supergroup symmetry is studied based on the Bethe ansatz solution of the related vertex model. This model is a lattice realization of intersecting loops in two dimensions with loop…
A numerical study is presented of the 3d Gaussian Random Field Ising Model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on…
Finite size effects in Euclidean ${\rm CP}^{N-1}$ models with periodic boundary conditions are investigated by means of the $1/N$ expansion and by Monte Carlo simulations. Analytic and numerical results for magnetic susceptibility and…
We propose very efficient algorithms for the bootstrap percolation and the diffusion percolation models by extending the Newman-Ziff algorithm of the classical percolation [M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. 85 (2000) 4104].…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
We study zero-range processes which are known to exhibit a condensation transition, where above a critical density a non-zero fraction of all particles accumulates on a single lattice site. This phenomenon has been a subject of recent…
We study bootstrap inference for the $k$th largest coordinate of a normalized sum of independent high-dimensional random vectors. Existing second-order theory for maxima does not directly extend to order statistics, because the event…
We study a percolation model on the square lattice, where clusters "freeze" (stop growing) as soon as their volume (i.e. the number of sites they contain) gets larger than N, the parameter of the model. A model where clusters freeze when…
Using Finite-Size Scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention in parameterizing the corrections-to-scaling, what is…
We postulate the existence of a natural Poissonian marking of the double (touching) points of SLE(6) and hence of the related continuum nonsimple loop process that describes macroscopic cluster boundaries in 2D critical percolation. We…
In this note we analyze an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model…
We present a Monte Carlo study of the one-component $\phi^4$ model on the cubic lattice in three dimensions. Leading order scaling corrections are studied using the finite size scaling method. We compute the corrections to scaling exponent…
Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…
The physics of $k$-core percolation pertains to those systems whose constituents require a minimum number of $k$ connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from…
We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance ${\bf r}$ in the finite system with size $L$, the correlation function can be written as the product of $|{\bf…
A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold $p_c\approx 0.655$ is found between…