Dgsos on DTRS

We perform simulations of a discrete gaussian solid on solid (DGSOS) model on dynamical ${\varphi }^3$ graphs, which is equivalent to coupling the model to 2d quantum gravity, using the cluster algorithms recently developed by Evertz et.al.for use on fixed lattices. We find evidence from the growth of the width-squared in the rough phase of KT-like behaviour, which is consistent with theoretical expectations. We also investigate the cluster statistics, dynamical critical exponent and lattice properties, and compare these with the dual XY model.