English
Related papers

Related papers: The critical pulling force for self-avoiding walks

200 papers

We prove some theorems about self-avoiding walks attached to an impenetrable surface (i.e. positive walks) and subject to a force. Specifically we show the force dependence of the free energy is identical when the force is applied at the…

Statistical Mechanics · Physics 2016-02-17 EJ Janse van Rensburg , SG Whittington

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…

Statistical Mechanics · Physics 2009-11-07 D. P. Foster , F. Seno

Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…

Statistical Mechanics · Physics 2009-11-07 Peter Grassberger , Hsiao-Ping Hsu

We introduce a self-avoiding walk model for which end-effects are completely eliminated. We enumerate the number of these walks for various lattices in dimensions two and three, and use these enumerations to study the properties of this…

Statistical Mechanics · Physics 2015-04-09 Nathan Clisby

We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on…

Statistical Mechanics · Physics 2024-07-24 C J Bradly , N R Beaton , A L Owczarek

We propose and study a model of polymer chains in a bilayer. Each chain is confined in one of the layers and polymer bonds on first neighbor edges in different layers interact. We also define and comment results for a model with…

Statistical Mechanics · Physics 2015-06-05 Pablo Serra , Jürgen F. Stilck

Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks interacting with (alternate) sites on the surface of the honeycomb lattice is $1+\sqrt{2}$. A key identity…

Mathematical Physics · Physics 2015-06-03 Nicholas R. Beaton , Anthony J. Guttmann , Iwan Jensen

In this paper, we investigate a model for a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW. The interaction intensity and the free energy of the system are denoted by…

Probability · Mathematics 2015-07-29 P. Carmona , G. B. Nguyen , N. Pétrélis

We study the thermodynamics of an exactly solvable model of a self-interacting partially directed self-avoiding walk (DSAW) in two dimensions, when a force is applied on one end of the chain. The critical force for the unfolding is…

Statistical Mechanics · Physics 2009-11-10 A. Rosa , D. Marenduzzo , A. Maritan , F. Seno

We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we use to obtain large samples of walks on the cubic lattice of up to $33 \times 10^6$ steps. Consequently the critical exponent $\nu$ for…

Statistical Mechanics · Physics 2010-02-03 Nathan Clisby

We investigate the phase diagram of a self-avoiding walk model of a 3-star polymer in two dimensions, adsorbing at a surface and being desorbed by the action of a force. We show rigorously that there are four phases: a free phase, a…

Statistical Mechanics · Physics 2019-05-14 C J Bradly , E J Janse van Rensburg , A L Owczarek , S G Whittington

We solve a model of self-avoiding walks with up to two monomers per site on the Bethe lattice. This model, inspired on the Domb-Joyce model, was recently proposed to describe the collapse transition observed in interacting polymers [J.…

Statistical Mechanics · Physics 2009-11-11 Pablo Serra , Juergen F. Stilck

We show that the structural properties and phase behavior of a self-avoiding polymer chain on adhesive substrate, subject to pulling at the chain end, can be obtained by means of a Grand Canonical Ensemble (GCE) approach. We derive…

Soft Condensed Matter · Physics 2009-04-05 S. Bhattacharya , V. G. Rostiashvili , A. Milchev , T. A. Vilgis

We consider a directed walk model of a homopolymer (in two dimensions) which is self-interacting and can undergo a collapse transition, subject to an applied tensile force. We review and interpret all the results already in the literature…

Statistical Mechanics · Physics 2009-11-13 R. Brak , P. Dyke , J. Lee , A. L. Owczarek , T. Prellberg , A. Rechnitzer , S. G. Whittington

We study a model of a semiflexible long chain polymer confined to a two-dimensional slit of width $w$, and interacting with the walls of the slit. The interactions with the walls are controlled by Boltzmann weights $a$ and $b$, and the…

Statistical Mechanics · Physics 2019-12-03 Nicholas R. Beaton , Leo Li , Jonathon Liu , Thomas Wong

We consider a self-avoiding walk model (SAW) on the faces of the square lattice $\mathbb{Z}^2$. This walk can traverse the same face twice, but crosses any edge at most once. The weight of a walk is a product of local weights: each square…

Probability · Mathematics 2021-12-17 Alexander Glazman , Ioan Manolescu

The collapse transition of an isolated polymer has been modelled by many different approaches, including lattice models based on self-avoiding walks and self-avoiding trails. In two dimensions, previous simulations of kinetic growth trails,…

Statistical Mechanics · Physics 2009-11-11 A. L. Owczarek , T. Prellberg

We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous…

Statistical Mechanics · Physics 2019-01-02 C. J. Bradly , A. L. Owczarek , T. Prellberg

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…

Disordered Systems and Neural Networks · Physics 2007-05-23 Cecile Monthus

We consider self-avoiding lattice polygons, in the hypercubic lattice, as a model of a ring polymer adsorbed at a surface and either being desorbed by the action of a force, or pushed towards the surface. We show that, when there is no…

Statistical Mechanics · Physics 2018-02-14 AJ Guttmann , EJ Janse van Rensburg , I Jensen , SG Whittington