Renormalization theory of self-avoiding walks which cross a square
نویسندگان
چکیده
منابع مشابه
Self-avoiding walks crossing a square
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]× [0, L] on the square lattice Z. The number of distinct walks is known to grow as λ 2+o(L2). We estimate λ = 1.744550± 0.000005 as well as obtaining strict upper and lower bounds, 1.628 < λ < 1.782. We give exact results for the number of SAW o...
متن کاملEnumeration of self-avoiding walks on the square lattice
We describe a new algorithm for the enumeration of self-avoiding walks on the square lattice. Using up to 128 processors on a HP Alpha server cluster we have enumerated the number of self-avoiding walks on the square lattice to length 71. Series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and mean-square distance of monomers from the end points h...
متن کاملSquare lattice walks avoiding a quadrant
In the past decade, a lot of attention has been devoted to the enumeration of walks with prescribed steps confined to a convex cone. In two dimensions, this means counting walks in the first quadrant of the plane (possibly after a linear transformation). But what about walks in non-convex cones? We investigate the two most natural cases: first, square lattice walks avoiding the negative quadran...
متن کاملAnisotropic Self - Avoiding Walks
We consider a model of self-avoiding walks on the lattice Zd with different weights for steps in each of the 2d lattice directions. We find that the directiondependent mass for the two-point function of this model has three phases: mass positive in all directions; mass identically −∞; and masses of different signs in different directions. The final possibility can only occur if the weights are ...
متن کاملPrudent Self-Avoiding Walks
We have produced extended series for prudent self-avoiding walks on the square lattice. These are subsets of self-avoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic) generating function is almost certainly not differentiably-finite.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1991
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/24/21/021