Related papers: A parallel algorithm for the enumeration of self-a…
We have extended the enumeration of self-avoiding walks on the Manhattan lattice from 28 to 53 steps and for self-avoiding polygons from 48 to 84 steps. Analysis of this data suggests that the walk generating function exponent gamma =…
Exactly solvable models of planar polygons, weighted by perimeter and area, have deepened our understanding of the critical behaviour of polygon models in recent years. Based on these results, we derive a conjecture for the exact form of…
We give an algorithm for counting self-avoiding walks or self-avoiding polygons that runs in time $\exp(C\sqrt{n\log n})$ on 2-dimensional lattices and time $\exp(C_dn^{(d-1)/d}\log n)$ on $d$-dimensional lattices for $d>2$.
We study the exact counting problem for all lattice rectangles contained in the square $[0,n)\times[0,n)$, including non-axis-parallel ones. Starting from the standard parametrization by a primitive direction $(u,v)$ and two side lengths,…
Self-avoiding walks on the body-centered-cubic (BCC) and face-centered-cubic (FCC) lattices are enumerated up to lengths 28 and 24, respectively, using the length-doubling method. Analysis of the enumeration results yields values for the…
We show how to compute the generating function of the self-avoiding polygons on a lattice by using the statistical mechanics Schwinger-Dyson equations for the correlation functions of the $N$-vector spin model on that lattice.
We discuss the probability of random knotting for a model of self-avoiding polygons whose segments are given by cylinders of unit length with radius $r$. We show numerically that the characteristic length of random knotting is roughly…
A new algorithm for the derivation of low-density expansions has been used to greatly extend the series for moments of the pair-connectedness on the directed square lattice near an impenetrable wall. Analysis of the series yields very…
Theta-graphs are a type of spatial graph with two vertices connected by three edges. We investigate embeddings of theta-graphs in the square and simple cubic lattices, using a combination of the Wang-Landau Monte Carlo method with a variant…
Analog layout synthesis requires some elements in the circuit netlist to be matched and placed symmetrically. However, the set of symmetries is very circuit-specific and a versatile algorithm, applicable to a broad variety of circuits, has…
I develop a transfer matrix algorithm for computing the exact partition function of a square lattice polymer with nearest-neighbor interaction, by extending a previous algorithm for computing the total number of self-avoiding walks. The…
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…
Enumerating polygons on regular lattices is a classic problem in rigorous statistical mechanics. The goal of enumerating polygons on the square lattice via fermionic path integration was achieved using a free-fermion quadratic action in the…
We build upon a recent theoretical breakthrough by employing novel algorithms to accurately compute the fractions $F_p$ of all closed walks on the infinite square lattice whose the last erased loop corresponds is any one of the $762, 207,…
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 present a space and time efficient practical parallel algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. The core of the algorithm is a…
We introduce a two-dimensional lattice model for the description of knotted polymer rings. A polymer configuration is modeled by a closed polygon drawn on the square diagonal lattice, with possible crossings describing pairs of strands of…
We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This allows the heuristic recovery of several algebraic…
We investigate the application of quantum computing algorithms to enhance the efficiency of enumerating self-avoiding walks (SAWs), utilizing quantum properties such as superposition and interference. A Quantum Amplitude Estimation…
We use the recently conjectured exact $S$-matrix of the massive ${\rm O}(n)$ model to derive its form factors and ground state energy. This information is then used in the limit $n\to0$ to obtain quantitative results for various universal…