Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the growth constant for square-lattice self-avoiding walks   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-Matrix method, due to another of us (JLJ). We show this to
be the most computationally efficient of the three methods, and by
parallelising the algorithm we have estimated the growth constant significantly
more precisely, incidentally ruling out the conjecture, which fails in the 12th
digit. Our new estimate of the growth constant is $$\mu(\mathrm{square}) =
2.63815853032790\, (3).$$

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The categories of this paper are: ao-sci
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The categories of this paper are: physics
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
9
The categories of this paper are: nlin