The connective constant of a transitive graph is the exponential growth rate of its number of self-avoiding walks. We prove that the set of connective constants of the so-called Cayley graphs contains a Cantor set. In particular, this set has the cardinality of the continuum.
"The set of connective constants of Cayley graphs contains a Cantor space." Electron. Commun. Probab. 22 1 - 4, 2017. https://doi.org/10.1214/17-ECP43