The critical behaviour of two-dimensional self-avoiding random walks

We present exact results for the mean end-to-end distance of self-avoiding random walks on several planar lattices. For the square lattice, we extend the known results from walks with ≦20 steps to walks with ≦22 steps, and for the triagular lattice from 14 to 16 steps. For the honeycomb lattice we went up to 34 steps, for the two-choice square lattice up to 44 steps, and for the 4-choice triagular lattice up to 19 steps. The extrapolated valuev=0.747±0.001 (provided the correction-to-scalng exponent is not appreaciably smaller than unity) is in disagreement with both Flory's value and the recent estimate of Derrida. We claim that a different analysis of Derrida's data supports this value.