  We study the phase diagrams of a family of 3D "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 analogue of the confining
transition in the Walker-Wang models can therefore lead to bulk deconfinement
and topological order.
