Square Lattice Self-Avoiding Walks and Corrections to Scaling

Abstract

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 $\ensuremath{\Delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{3}{2}.$