相关论文: Berezinskii-Kosterlitz-Thouless-like percolation t…
We study the contact process on the long-range percolation cluster on $\mathbb{Z}$ where each edge $\langle i,j \rangle$ is open with probability $|i-j|^{-s}$ for $s> 2$. Using a renormalization procedure we apply Peierls-type argument to…
Within the framework of the effective potential theory of the structural glass transition, we calculate for the p-spin model a static nonlinear susceptibility related to a four-point density correlation function, and show that it grows and…
Percolation models with multiple percolating clusters have attracted much attention in recent years. Here we use Monte Carlo simulations to study bond percolation on $L_{1}\times L_{2}$ planar random lattices, duals of random lattices, and…
The Berezinskii-Kosterlitz-Thouless (BKT) transition is an archetypal example of a topological phase transition, which is driven by the proliferation of vortices. In this Letter, we analyze the persistence of the BKT transition in the XY…
In statistical physics, the XY model in two dimensions provides the paradigmatic example of phase transitions mediated by topological defects (vortices). Over the years, a variety of analytical and numerical methods have been deployed in an…
Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii--Kosterlitz--Thouless phase transitions of the two-dimensional (2D) classical $XY$ and the 2D generalized classical…
We investigate the out of equilibrium dynamics of the two-dimensional XY model when cooled across the Berezinskii-Kosterlitz-Thouless (BKT) phase transition using different protocols. We focus on the evolution of the growing correlation…
Under some general assumptions, we construct the scaling limit of open clusters and their associated counting measures in a class of two dimensional percolation models. Our results apply, in particular, to critical Bernoulli site…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
We consider the percolation problem of sites on an $L\times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N=uL^2$ steps, i.e. are vacant. Most of the results are obtained from numerical…
We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an…
We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…
We perform Monte Carlo simulations to determine the average excluded area $<A_{ex}>$ of randomly oriented squares, randomly oriented widthless sticks and aligned squares in two dimensions. We find significant differences between our results…
Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…
In this work, we proposed and experimentally demonstrated a photonic simulator for XY models, which is a typical kind of classical spin models. By encoding the XY spins on the phase term of the input light field, the corresponding XY…
Using grand canonical Monte Carlo simulations, we investigate the percolation behavior of a square well fluid with an ultra-short range of attraction in three dimension (3D) and in confined geometry. The latter is defined through two…
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…
Using Monte Carlo methods, we compute the finite-size scaling function of the helicity modulus $\Upsilon$ of the two-dimensional O(3) model and compare it to the low temperature expansion prediction. From this, we estimate the range of…
We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond…
We perform Monte-Carlo simulations to study the Bernoulli ($p$) bond percolation on the enhanced binary tree which belongs to the class of nonamenable graphs with one end. Our numerical results show that the system has two different…