Self-avoiding walks and trees in spread-out lattices |
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| Authors: | Mathew D Penrose |
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| Institution: | (1) Department of Mathematical Sciences, University of Durham, DH1 3LE Durham, England |
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| Abstract: | LetG
R
be the graph obtained by joining all sites ofZ
d which are separated by a distance of at mostR. Let  (G
R
) denote the connective constant for counting the self-avoiding walks in this graph. Let  (G
R
) denote the coprresponding constant for counting the trees embedded inG
R
. Then asR  , (G
R
) is asymptotic to the coordination numberk
R ofG
R
, while (G
R
) is asymptotic toek
R. However, ifd is 1 or 2, then (G
R
)-k
R
diverges to –.Dedicated to Oliver Penrose on this occasion of his 65th birthday. |
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| Keywords: | Self-avoiding random walk connective constant mean-field behavior trees polymers |
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