Related papers: Interacting Growth Walk on a honeycomb lattice
We investigate, by series methods, the behaviour of interacting self-avoiding walks (ISAWs) on the honeycomb lattice and on the square lattice. This is the first such investigation of ISAWs on the honeycomb lattice. We have generated data…
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…
We show that the compact self avoiding walk configurations, kinetically generated by the recently introduced Interacting Growth Walk (IGW) model, can be considered as members of a canonical ensemble if they are assigned random values of…
We have explained in detail why the canonical partition function of Interacting Self Avoiding Walk (ISAW), is exactly equivalent to the configurational average of the weights associated with growth walks, such as the Interacting Growth Walk…
We show that the Density of States (DoS) for lattice Self Avoiding Walks can be estimated by using an inverse algorithm, called flatIGW, whose step-growth rules are dynamically adjusted by requiring the energy histogram to be locally flat.…
Interacting Growth Walks is a recently proposed stochastic model for studying the coil-globule transition of linear polymers. We propose a flat energy histogram version for Interacting Growth Walk. We demonstrate the algorithm on two…
Interacting Self Avoiding Walk (ISAW) on a lattice is a simple model to study the Coil to Globule transition of linear homopolymers. The temperature at which the transition takes place is called the theta temperature. The value of theta…
This article is dedicated to the study of the 2-dimensional interacting prudent self-avoiding walk (referred to by the acronym IPSAW) and in particular to its collapse transition. The interaction intensity is denoted by $\beta>0$ and the…
A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and has a trapped endpoint. We show that the generating function enumerating GSAWs on a half-infinite strip of finite height is…
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…
A growing self-avoiding walk (GSAW) is a stochastic process that starts from the origin on a lattice and grows by occupying an unoccupied adjacent lattice site at random. A sufficiently long GSAW will reach a state in which all adjacent…
We find the generating function of self-avoiding walks and trails on a semi-regular lattice called the $3.12^2$ lattice in terms of the generating functions of simple graphs, such as self-avoiding walks, polygons and tadpole graphs on the…
We study a generalized interacting self-avoiding walk (ISAW) model with nearest- and next nearest-neighbor (NN and NNN) interactions on the square and cubic lattices. In both dimensions, the phase diagrams show coil and globule phases…
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…
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…
The smart kinetic self-avoiding walk (SKSAW) is a random walk which never intersects itself and grows forever when run in the full-plane. At each time step the walk chooses the next step uniformly from among the allowable nearest neighbors…
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…
We study a restricted class of self-avoiding walks (SAW) which start at the origin (0, 0), end at $(L, L)$, and are entirely contained in the square $[0, L] \times [0, L]$ on the square lattice ${\mathbb Z}^2$. The number of distinct walks…
We present analyses of substantially extended series for both interacting self-avoiding walks (ISAW) and polygons (ISAP) on the square lattice. We argue that these provide good evidence that the free energies of both linear and ring…
We review some recent results obtained in the framework of the 2-dimensional Interacting Self-Avoiding Walk (ISAW). After a brief presentation of the rigorous results that have been obtained so far for ISAW we focus on the Interacting…