  We show that the usefulness of the thermal state of a specific spin-lattice
model for measurement-based quantum computing exhibits a transition between two
distinct "phases" - one in which every state is a universal resource for
quantum computation, and another in which any local measurement sequence can be
simulated efficiently on a classical computer. Remarkably, this transition in
computational power does not coincide with any phase transition, classical or
quantum, in the underlying spin-lattice model.
