Using Monte Carlo techniques, we study $Z_N$ lattice gauge theory coupled to a Higgs field represented by spins situated on the lattice sites. We present phase diagrams for the $Z_2$ and $Z_6$ theories with Higgs field in the fundamental representation of the gauge group and for $Z_6$ gauge theory coupled to $Z_3$ Higgs fields.

• Received 27 August 1979

DOI:https://doi.org/10.1103/PhysRevD.21.1006