Self-avoiding walks

Imagine a solution of polymers. A good solvent allows the polymer chains to move freely and adopt different configurations. A fundamental geometrical property that can be used to characterize a polymer is the rms end-to-end distance $R_N$, where $N$ is the number of monomers.

A simple model to describe the global features of a polymer in a solution consists of same-size straight segments joined toghether at random angles. The most important feature of a polymer is that two monomers cannot occupy the same spatial position. This is precisely the property that defines the self-avoiding walk (SAW), a walk that starts from a point, subject to the global constraint that cannot visit the same site of the lattice more than once during the walk.