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 3N/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.