  We study the effect of adding a matter field to the Z2 gauge model in three
dimensions at zero and finite temperature. Up to a given value of the parameter
regulating the coupling, the matter field produces a slight shift of the
transition line without changing the universality class of the pure gauge
theory, as seen by finite size scaling analysis or by comparison, in the finite
temperature case, to exact formulas of conformal field theory. At zero
temperature the critical line turns into a first-order transition. The fate of
this kind of transition in the finite temperature case is discussed.
