arXiv subjects

A R Conway

Publications and source records attributed to A R Conway.

2 recordsLinked to original sources

arXiv1992

Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice

We 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 $3^{N/4}$ times a polynomial in $N$, and so the approach is greatly superior to direct counting techniques. We have enumerated walks of up to 39 steps. As a consequence, we are able to accurately estimate the critical point, critical exponent, and critical amplitude.

hep-lat↗

arXiv1992

Enumeration of self avoiding trails on a square lattice using a transfer matrix technique

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 $A λ^n n^{11 \over 32}$, we find $λ= 2.72062 \pm 0.000006$ and $A = 1.272 \pm 0.002$.

hep-lat↗