Related papers: Two-dimensional interacting self-avoiding walks: n…
We derive the nested Bethe Ansatz solution of the fully packed O($n$) loop model on the honeycomb lattice. From this solution we derive the bulk free energy per site along with the central charge and geometric scaling dimensions describing…
Two closely related models of oriented self-avoiding walks (OSAWs) on a square lattice are studied. We use the pruned-enriched Rosenbluth method to determine numerically the phase diagram. Both models have three phases: a tight-spiral phase…
Monte Carlo simulations, using the PERM algorithm, of interacting self-avoiding walks (ISAW) and interacting self-avoiding trails (ISAT) in five dimensions are presented which locate the collapse phase transition in those models. It is…
The partition function of the O(n) loop model on the honeycomb lattice is mapped to that of the O(n) loop model on the 3-12 lattice. Both models share the same operator content and thus critical exponents. The critical points are related…
We consider nearest-neighbor self-avoiding walk, bond percolation, lattice trees, and bond lattice animals on ${\mathbb{Z}}^d$. The two-point functions of these models are respectively the generating function for self-avoiding walks from…
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 give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice $Z^d$. The method is based on loop erasure and restoration, and does not require exact…
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…
This article is concerned with self-avoiding walks (SAW) on $\mathbb{Z}^{d}$ that are subject to a self-attraction. The attraction, which rewards instances of adjacent parallel edges, introduces difficulties that are not present in ordinary…
The phase diagram and surface critical behaviour of the vertex-interacting self-avoiding walk are examined using transfer matrix methods extended using DMRG and coupled with finite-size scaling. Particular attention is paid to the critical…
For the hard-core lattice gas model defined on independent sets weighted by an activity $\lambda$, we study the critical activity $\lambda_c(\mathbb{Z}^2)$ for the uniqueness/non-uniqueness threshold on the 2-dimensional integer lattice…
We show numerically that critical exponents for two-point interchain correlation of an infinite chain characterize those of finite chains in Self-Avoiding Walk (SAW) and Self-Avoiding Polygon (SAP) under a topological constraint. We…
We calculate the connective constant for self-avoiding walks on the simple cubic lattice to unprecedented accuracy, using a novel application of the pivot algorithm. We estimate that \mu = 4.684 039 931(27). Our method also provides…
Self-avoiding walks and self-avoiding trails, two models of a polymer coil in dilute solution, have been shown to be governed by the same universality class. On the other hand, self-avoiding walks interacting via nearest-neighbour contacts…
We introduce classes of restricted walks, surfaces and their generalisations. For example, self-osculating walks (SOWs) are supersets of self-avoiding walks (SAWs) where edges are still not allowed to cross but may 'kiss' at a vertex. They…
We develop an approach for performing scaling analysis of $N$-step Random Walks (RWs). The mean square end-to-end distance, $\langle\vec{R}_{N}^{2}\rangle$, is written in terms of inner persistence lengths (IPLs), which we define by the…
We investigate polymers pulled away from an interacting surface, where the force is applied to the untethered endpoint and at an angle $\theta$ to the surface. We use the canonical self-avoiding walk model of polymers and obtain the phase…
We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W_n(S), and rooted…
We consider the model of self-avoiding walks on the $d$-dimensional hypercubic lattice interacting with a $d^*$-dimensional defect, where $1\leq d^*<d$. Such an interaction can be attractive or repulsive, and is controlled by a Boltzmann…
We present simulations of self-avoiding random walks on 2-d lattices with the topology of an infinitely long cylinder, in the limit where the cylinder circumference L is much smaller than the Flory radius. We study in particular the…