Quantum-computational universality and quantum phase transitions in the ground states of spin lattices

We investigate spin-lattice models for which the ground state is a universal resource for measurement-based quantum computing (MBQC). We investigate the existence of models with a computationally-universal quantum phase, i.e., models that exhibit a quantum phase transition and for which every ground state in one of its phases is a universal resource for a single common MBQC model.