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

Comments: To be published in J. Phys. A:Math Gen. Pages: 16 Format: RevTeX