New data and analysis of a 51-term series for self-avoiding walks on the (anisotropic) square lattice is given. Analysis of the series provides compelling evidence that the generating function for walks cannot be written as an algebraic or $D$-finite function and that the correction-to-scaling exponent is $\Delta =\frac{3}{2}.$

• Received 14 August 1996

DOI:https://doi.org/10.1103/PhysRevLett.77.5284