Connective constant

Summary

The connective constant of a lattice is the exponential growth rate of the number of self-avoiding walks on it. Let $c_n$ be the number of self-avoiding walks of $n$ steps from a fixed vertex. Then $c_n$ grows like $\mu^n$, and $\mu$ is the connective constant. It is a basic quantity in the study of polymers and of critical phenomena on lattices. Its exact value is known for very few lattices, the main one being the hexagonal lattice.