[en] We study the Z₂ lattice gauge theory coupled to scalar matter fields (Ising spins) in 2+1 dimensions. Strong-coupling expansions are obtained for the masses of both ''meson'' and ''glueball'' excitations. We use the zeros of the mass gap, obtained using Pade approximants and duality transformations, to locate second-order phase transitions as a function of the gauge and matter coupling constants. The resulting phase diagram is in reasonable agreement with that obtained by other methods. These other methods (Monte Carlo and 1/N expansions) are, however, most sensitive to first-order phase transitions while our method is most sensitive to continuous phase transitions. We observe that the additional parameter of the Hamiltonian approach is essentially irrelevant