Osmotic pressure of confined square lattice self-avoiding walks
نویسندگان
چکیده
منابع مشابه
Enumeration 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...
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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...
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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...
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A self-avoiding walk on an infinitely long lattice strip of finite width will asymptotically exhibit an end-to-end separation proportional to the number of steps. A proof of this proposition is presented together with comments concerning an earlier attempt to deal with the matter. In addition, some unproved, yet "obvious," conjectures concerning self-avoiding walks are cited as basic propositio...
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We have developed an improved algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 90. Analysis of the resulting series yields very accurate estimates of the connective constant μ = 2.638 158 529 27(1) (biased) and the critical exponent α = 0.500 0005(10) (unbiased). The critical point is indistinguishable from a root of the polyno...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2018
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8121/aaf065