Related papers: Self-Avoiding Walk on the square site-diluted Isin…
Let Z_N be the number of self-avoiding paths of length N starting from the origin on the infinite cluster obtained after performing Bernoulli percolation on Z^d with parameter p>p_c(Z^d). The object of this paper is to study the connective…
We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on $\mathbb{Z}^4$, for sufficiently small attraction. We prove that the susceptibility and correlation length of order $p$ (for…
We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated Ising system where they occupy site vacancies. Fermions interact via local spin fluctuations and we analyze coupled self-consistent mean-field…
Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are…
The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are…
Lattice model of directed self avoiding walk is used to investigate adsorption properties of a semiflexible sequential copolymer chain on an impenetrable curved surface on a hexagonal lattice in two dimensions. Walks of the copolymer chains…
Correlations between two variables of a high-dimensional system can be indicative of an underlying interaction, but can also result from indirect effects. Inverse Ising inference is a method to distinguish one from the other. Essentially,…
This is the second of two papers on the end-to-end distance of a weakly self-repelling walk on a four dimensional hierarchical lattice. It completes the proof that the expected value grows as a constant times \sqrt{T} log^{1/8}T (1+O((log…
The solvability of the three-dimensional O($N$) scalar field theory in the large $N$ limit makes it an ideal toy model exhibiting "walking" behavior, expected in some SU($N$) gauge theories with a large number of fermion flavors. We study…
We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We…
We propose an algorithm based on local growth rules for kinetically generating self avoiding walk configurations at any given temperature. This algorithm, called the Interacting Growth Walk (IGW) algorithm, does not suffer from attrition on…
In this paper, we study the abundance of self-avoiding paths of a given length on a supercritical percolation cluster on $\bbZ^d$. More precisely, we count $Z_N$ the number of self-avoiding paths of length $N$ on the infinite cluster,…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for…
A transfer matrix scaling technique is developed for randomly diluted systems, and applied to the site-diluted Ising model on a square lattice in two dimensions. For each allowed disorder configuration between two adjacent columns, the…
Monte Carlo cluster algorithms are popular for their efficiency in studying the Ising model near its critical temperature. We might expect that this efficiency extends to the bond-diluted Ising model. We show, however, that this is not…
Prudent walks are self-avoiding walks which cannot step towards an already occupied vertex. We introduce a new model of adsorbing prudent walks on the square lattice, which start on an impenetrable surface and accrue a fugacity $a$ with…
Understanding phase transitions requires not only identifying order parameters but also characterizing how their correlations behave across scales. By quantifying how fluctuations at distinct spatial or temporal points are related,…
We consider the backbone of the infinite cluster generated by supercritical oriented site percolation in dimension 1 +1. A directed random walk on this backbone can be seen as an "ancestral line" of an individual sampled in the stationary…
Geometric representations provide a useful perspective on critical phenomena in the Ising model. In a recent study [Phys. Rev. E 112, 034118 (2025)], we found that the two-dimensional critical Ising model exhibits two consecutive…