  We construct a 2D quantum spin model that realizes an Ising paramagnet with
gapless edge modes protected by Ising symmetry. This model provides an example
of a "symmetry-protected topological phase." We describe a simple physical
construction that distinguishes this system from a conventional paramagnet: we
couple the system to a Z_2 gauge field and then show that the \pi-flux
excitations have different braiding statistics from that of a usual paramagnet.
In addition, we show that these braiding statistics directly imply the
existence of protected edge modes. Finally, we analyze a particular microscopic
model for the edge and derive a field theoretic description of the low energy
excitations. We believe that the braiding statistics approach outlined in this
paper can be generalized to a large class of symmetry-protected topological
phases.
