Geometric Order in Quantum Multigraphs

Quantum Multigraphs are combinatorially defined Hilbert spaces whose basis vectors are in a one-to-one correspond with classical multigraphs. They are constructed as possible microstates for Background Independent formulations of quantum gravity. We find a recursively defined Hamiltonian on quantum multigraphs whose ground states are combinatorial manifolds. We examine thermodynamic properties this Hamiltonian through Monte Carlo simulations and present evidence that the system is gapless and has a quantum critical phase.