Enumeration of compact self-avoiding walks
نویسنده
چکیده
We have developed a transfer matrix algorithm for the enumeration of compact self-avoiding walks on rectangular strips of the square lattice. The algorithm is easily adapted to other shapes or generalized to problems such as interacting walks. These models are relevant in the study of globular proteins. 2001 Elsevier Science B.V. All rights reserved. PACS: 05.50.+q; 02.70.Rw; 61.25.Hq
منابع مشابه
Multicanonical simulation of the Domb-Joyce model and the Go model: new enumeration methods for self-avoiding walks
We develop statistical enumeration methods for self-avoiding walks using a powerful sampling technique called the multicanonical Monte Carlo method. Using these methods, we estimate the numbers of the two dimensional N-step self-avoiding walks up to N = 256 with statistical errors. The developed methods are based on statistical mechanical models of paths which include self-avoiding walks. The c...
متن کاملSelf-avoiding walks and polygons on quasiperiodic tilings
We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices, these numbers depend on the chosen initial vertex. We compare different ways of counting and demonstrate that suitable averaging improves convergence to the asym...
متن کاملSelf-avoiding walk enumeration via the lace expansion
We introduce a new method for the enumeration of self-avoiding walks based on the lace expansion. We also introduce an algorithmic improvement, called the two-step method, for self-avoiding walk enumeration problems. We obtain significant extensions of existing series on the cubic and hypercubic lattices in all dimensions d ≥ 3: we enumerate 32-step self-avoiding polygons in d = 3, 26-step self...
متن کاملStochastic Enumeration and Splitting Methods for Counting Self-Avoiding Walks
We present a new method for counting self-avoiding walks (SAW’s), called stochastic enumeration (SE), a stochastic replica of the naive (computationally intractable) full enumeration method. Also presented is a new approach, called OSLA-SPLIT, a combination of classic splitting with importance sampling. The latter is based on the well-known method, onestep-look-ahead (OSLA) method. Polynomial c...
متن کاملImproved lower bounds on the connective constants for two-dimensional self-avoiding walks
We calculate improved lower bounds for the connective constants for selfavoiding walks on the square, hexagonal, triangular, (4.82) and (3.122) lattices. The bound is found by Kesten’s method of irreducible bridges. This involves using transfer-matrix techniques to exactly enumerate the number of bridges of a given span to very many steps. Upper bounds are obtained from recent exact enumeration...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001