Related papers: The critical pulling force for self-avoiding walks
The model of self-avoiding lattice walks and the asymptotic analysis of power-series have been two of the major research themes of Tony Guttmann. In this paper we bring the two together and perform a new analysis of the generating functions…
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…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…
We study several models of staircase polygons on the $45^\circ$ rotated square lattice, which interact with an impenetrable surface while also being pushed towards or pulled away from the surface by a force. The surface interaction is…
Lattice model of directed self avoiding walk has been solved analytically to investigate adsorption desorption phase transition behaviour of a semiflexible sequential copolymer chain on a two dimensional impenetrable surface perpendicular…
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…
We perform a numerical study of a new microcanonical polymer model on the three dimensional cubic lattice, consisting of ideal chains whose range and number of nearest-neighbor contacts are fixed to given values. Our simulations suggest an…
Some time ago Salmhofer demonstrated the equivalence of the strong coupling lattice Schwinger model with Wilson fermions to a certain 8-vertex model which can be understood as a self-avoiding loop model on the square lattice with bending…
We show that when a self-avoiding polymer chain is pulled off a sticky surface by force applied to the end segment, it undergoes a first-order thermodynamic phase transition albeit without phase coexistence. This unusual feature is…
The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=\pm Ct^\alpha. Using a scaling argument, 1/C is shown to be a marginal variable when \alpha=\nu_\perp/\nu_\parallel=1/2,…
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the…
In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our…
We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…
We study a lattice model of a magnetic polymer where the XY spin variables are located on a self-avoiding walk (SAW) on a regular lattice in two and three dimensions. We consider the regime where both spins and conformations are dynamic,…
In a recent letter, a simple method was proposed to generate solvable models that predict the critical properties of statistical systems in hyperspherical geometries. To that end, it was shown how to reduce a random walk in $D$ dimensions…
We implement a scale-free version of the pivot algorithm and use it to sample pairs of three-dimensional self-avoiding walks, for the purpose of efficiently calculating an observable that corresponds to the probability that pairs of…
We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if…
Flory-Huggins theory is a mean field theory for modelling the free energy of dense polymer solutions and polymer melts. In this paper we use Flory-Huggins theory as a model of a dense two dimensional self-avoiding walk confined to a square…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
This is a rather personal review of the problem of self-avoiding walks and polygons. After defining the problem, and outlining what is known rigorously and what is merely conjectured, I highlight the major outstanding problems. I then give…