Past exam of the quantum condensed matter course of the University of Cambridge / 2008 / Section A / A4 / a / ii / Solution

A planar self-avoiding walk cannot revisit its occupied sites. In the good-solvent scaling regime, the two-dimensional Flory approximation gives $R\sim b{N}^{3/4}$, larger at large $N$ than either ideal walk and the projected three-dimensional self-avoiding walk. This is a scaling statement, with microscopic prefactors dependent on the walk model.