  We report a new type of multicritical point that arises from competition
between the Higgs and confinement transitions in a Z_2 gauge system. The phase
diagram of the 3d gauge Higgs model has been obtained by Monte-Carlo simulation
on large (up to 60^3) lattices. We find the transition lines continue as
2nd-order until merging into a 1st-order line. These findings pose the question
of an effective field theory for a multicritical point involving noncommuting
order parameters. A similar phase diagram is predicted for the 2-dimensional
quantum toric code model with two external fields, h_z and h_x; this problem
can be mapped onto an anisotropic 3D gauge Higgs model.
