Phase structure of a Z2 lattice gauge theory coupled to a radially variable scalar field

Using Monte Carlo techniques and mean field method, we study a coupled Z₂ gauge-scalar system on a lattice without freezing the radial mode of the scalar field. We find that the phase diagram for our model makes a decided contrast with that for the coupled gauge-spin model when the self-coupling of the scalar field is small. First-order phase transitions caused by the radial fluctuation of the scalar field are observed.