Branched polymers, complex spins and the freezing transition

We show that by coupling complex three-state systems to branched-polymer like ensembles we can obtain models with γstr different from 12. It is also possible to study the interpolation between dynamical and crystalline graphs for these models; we find that only when geometry fluctuations are completely forbidden is there a crystalline phase. These models share many of the properties of full two-dimensional quantum gravity.