Algebraic techniques for enumerating self-avoiding walks on the square lattice
- 7 April 1993
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 26 (7) , 1519-1534
- https://doi.org/10.1088/0305-4470/26/7/012
Abstract
The authors describe a new algebraic technique for enumerating self-avoiding walks on the rectangular lattice. The computational complexity of enumerating walks of N steps is of order 3N/4 times a polynomial in N, and so the approach is greatly superior to direct counting techniques. They have enumerated walks of up to 39 steps. As a consequence, they are able to accurately estimate the critical point, critical exponent, and critical amplitude.Keywords
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