Enumeration of self-avoiding trails on a square lattice using a transfer matrix technique
- 7 April 1993
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 26 (7) , 1535-1552
- https://doi.org/10.1088/0305-4470/26/7/013
Abstract
We describe a new algebraic technique, utilising transfer matrices, for enumerating self-avoiding lattice trails on the square lattice. We have enumerated trails to 31 steps, and find increased evidence that trails are in the self-avoiding walk universality class. Assuming that trails behave like $A lambda ^n n^{11 over 32}$, we find $lambda = 2.72062 pm 0.000006$ and $A = 1.272 pm 0.002$.
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