Phase transitions in topological lattice models via topological symmetry breaking

We study transitions between phases of matter with topological order. By studying these transitions in exactly solvable lattice models we show how universality classes may be identified and critical properties described. As a familiar example to elucidate our results concretely, we describe in detail a transition between a fully gapped achiral 2D p-wave superconductor (p + ip for pseudo-spin up/p - ip for pseudo-spin down) to an s-wave superconductor. We show in particular that this transition is of the 2D transverse field Ising universality class.