Algorithmic tools for simulations of vertex models on random graphs

We consider the coupling of ice-type vertex models to random, planar φ4 quantum-gravity graphs. The well-established techniques for the simulation of dynamical triangulations and their dual φ3 graphs are suitably adapted to the case of four-valent graphs. These methods are combined with a formulation of the loop algorithm for the simulation of the vertex model matter part. We present a preliminary analysis of the dynamical scaling behaviour of the combined algorithm for the case of the 6-vertex model coupled to quantum gravity.