Monte Carlo calculations onZ2gauge-Higgs theories

Monte Carlo calculations have been carried out on $Z_2$ lattice gauge theories in $d=3\mathrm{}$ and $d=4\mathrm{}$ space-time dimensions. For $d=3\mathrm{}$, for the gauge-Higgs system, the results show a phase diagram in which the Higgs and confined regions are smoothly connected. There are lines of phase transitions surrounding the unconfined region; first-order behavior occurs on and near the self-dual line. For $d=4\mathrm{}$, for the pure gauge system, we confirm the results of Creutz et al., that the transition between confined and unconfined regions is first order.