Efficiency of the Incomplete Enumeration algorithm for Monte-Carlo simulation of linear and branched polymers

Details Efficiency of the Incomplete Enumeration algorithm for Monte-Carlo simulation of linear and branched polymers Efficiency of the Incomplete Enumeration algorithm for Monte-Carlo simulation of linear and branched polymers

2004-08-29

arxiv.org/abs/cond-mat/0408640v2

JSP, Vol 120,71-100(2005)

Physics

Condensed Matter

Statistical Mechanics

replaced with published version

Scientific paper

10.1007/s10955-005-5462-2

We study the efficiency of the incomplete enumeration algorithm for linear and branched polymers. There is a qualitative difference in the efficiency in these two cases. The average time to generate an independent sample of $n$ sites for large $n$ varies as $n^2$ for linear polymers, but as $exp(c n^{\alpha})$ for branched (undirected and directed) polymers, where $0<\alpha<1$. On the binary tree, our numerical studies for $n$ of order $10^4$ gives $\alpha = 0.333 \pm 0.005$. We argue that $\alpha=1/3$ exactly in this case.

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