Phase transitions in three-dimensional topological lattice models with surface anyons

We study the phase diagrams of a family of three-dimensional Walker-Wang-type lattice models, which are not topologically ordered but have deconfined anyonic excitations confined to their surfaces. We add a perturbation (analogous to that which drives the confining transition in Z(p) lattice gauge theories) to the Walker-Wang Hamiltonians, driving a transition in which all or some of the variables associated with the loop-gas or string-net ground states of these models become confined. We show that in many cases the location and nature of the phase transitions involved is exactly that of a generalized Z(p) lattice gauge theory, and use this to deduce the basic structure of the phase diagram. We further show that the relationship between the phases on opposite sides of the transition is fundamentally different than in conventional gauge theories: in the Walker-Wang case, the number of species of excitations that are deconfined in the bulk can increase across a transition that confines only some of the species of loops or string nets. The analog of the confining transition in the Walker-Wang models can therefore lead to bulk deconfinement and topological order.