How to Estimate the Number of Self-Avoiding Walks over 10100? Use Random Walks

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概要

• 論文の詳細を見る

• Counting the number of N-step self-avoiding walks (SAWs) on a lattice is one of the most difficult problems of enumerative combinatorics. Once we give up calculating the exact number of them, however, we have a chance to apply powerful computational methods of statistical mechanics to this problem. In this paper, we develop a statistical enumeration method for SAWs using the multicanonical Monte Carlo method. A key part of this method is to expand the configuration space of SAWs to random walks, the exact number of which is known. Using this method, we estimate a number of N-step SAWs on a square lattice, cN, up to N=256. The value of c256 is 5.6(1)× 10108 (the number in the parentheses is the statistical error of the last digit) and this is larger than one googol (10100).

著者

• Kikuchi Macoto

  Graduate School Of Science Osaka University:cybermedia Center Osaka University:graduate School Of Fr

• Shirai Nobu

  Graduate School Of Science Osaka University:cybermedia Center Osaka University

• KIKUCHI Macoto

  Graduate School of Science, Osaka University

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• How to Estimate the Number of Self-Avoiding Walks over 10100? Use Random Walks

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