Related papers: Structural Properties of Self-Attracting Walks
We consider various two-dimensional lattices such as square, Kagome, Lieb, honeycomb, dice lattices of finite extent, to study the effect of lattice profile in terms of the number of nearest neighbour and connectivity patterns on the…
Oriented self-avoiding walks (OSAWs) on a square lattice are studied, with binding energies between steps that are oriented parallel across a face of the lattice. By means of exact enumeration and Monte Carlo simulation, we reconstruct the…
We study via Monte Carlo simulation a generalisation of the so-called vertex interacting self-avoiding walk (VISAW) model on the square lattice. The configurations are actually not self-avoiding walks but rather restricted self-avoiding…
Consider a Brownian particle in three dimensions which is attracted by a plane with a strength proportional to some dimensionless parameter $\alpha$. We investigate the fractal spatial structure of the visited lattice sites in a cubic…
We define a new family of self-avoiding walks (SAW) on the square lattice, called weakly directed walks. These walks have a simple characterization in terms of the irreducible bridges that compose them. We determine their generating…
We consider the simple random walk on a random d-regular graph with n vertices, and investigate percolative properties of the set of vertices not visited by the walk until time un, where u > 0 is a fixed positive parameter. It was shown in…
Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…
The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by numerical simulations. We apply the pruned-enriched…
We perform a Monte Carlo simulation of two-dimensional N-step interacting self-avoiding walks at the theta point, with lengths up to N=3200. We compute the critical exponents, verifying the Coulomb-gas predictions, the theta-point…
We study Hamiltonian walks (HWs) on Sierpinski and $n$--simplex fractals. Via numerical analysis of exact recursion relations for the number of HWs we calculate the connectivity constant $\omega$ and find the asymptotic behaviour of the…
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model…
We study the sandpile model on three-dimensional spanning Ising clusters with the temperature $T$ treated as the control parameter. By analyzing the three dimensional avalanches and their two-dimensional projections (which show…
We consider the phase transition induced by compressing a self-avoiding walk in a slab where the walk is attached to both walls of the slab in two and three dimensions, and the resulting phase once the polymer is compressed. The process of…
It is widely believed that the scaling limit of self-avoiding walks (SAWs) at the critical temperature is (i) conformally invariant, and (ii) describable by Schramm-Loewner Evolution (SLE) with parameter $\kappa = 8/3.$ We consider SAWs in…
In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of…
We study loop erased random walk (LERW) on the percolation cluster, with occupation probability $p\geq p_c$, in two and three dimensions. We find that the fractal dimensions of LERW$_p$ is close to normal LERW in Euclidean lattice, for all…
In order to study long chain polymers many lattice models accommodate a pulling force applied to a particular part of the chain, often a free endpoint. This is in addition to well-studied features such as energetic interaction between the…
We study Hamiltonian walks (HWs) on the family of three--dimensional modified Sierpinski gasket fractals, as a model for compact polymers in nonhomogeneous media in three dimensions. Each member of this fractal family is labeled with an…
This paper is dedicated to the investigation of a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW and introduced in \cite{ZL68} by Zwanzig and Lauritzen to study the…
In the present paper, we consider the interacting partially-directed self-avoiding walk (IPDSAW) attracted by a vertical wall. The IPDSAW was introduced by Zwanzig and Lauritzen (J. Chem. Phys., 1968) as a manner of investigating the…