The phase diagram of the three-dimensional Z2 gauge Higgs system at zero and finite temperature

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.