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

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