Journal article
On the growth constant for square-lattice self-avoiding walks
JL Jacobsen, CR Scullard, AJ Guttmann
Journal of Physics A Mathematical and Theoretical | IOP PUBLISHING LTD | Published : 2016
Abstract
The growth constant for two-dimensional self-avoiding walks on the honeycomb lattice was conjectured by Nienhuis in 1982, and since that time the corresponding results for the square and triangular lattices have been sought. For the square lattice, a possible conjecture was advanced by one of us (AJG) more than 20 years ago, based on the six significant digit estimate available at the time. This estimate has improved by a further six digits over the intervening decades, and the conjectured value continued to agree with the increasingly precise estimates. We discuss the three most successful methods for estimating the growth constant, including the most recently developed topological transfer..
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Awarded by U.S. Department of Energy
Funding Acknowledgements
JLJ is grateful for the hospitality of the Centre of Excellence for Mathematics and Statistics of Complex Systems (Melbourne University) where part of this work was accomplished. He also acknowledges the support of the Institut Universitaire de France, and of the European Research Council through the Advanced Grant NuQFT. The work of CRS was performed under the auspices of the US Department of Energy at the Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. AJG acknowledges the support of the Australian Research Council through grant DP120100939. We thank Mireille Bousquet-Melou for the provision of a figure.