The Abelian Higgs model---a U(1) lattice gauge theory coupled to a fixed-length scalar field---is studied using Monte Carlo techniques. The phase diagram of the zero-temperature model on a four-dimensional Euclidean lattice is elucidated for systems with charge-one and charge-two Higgs fields. The order of various transitions is tentatively determined. Possible implications for quasiconfinement of quarks and gluons are also discussed briefly.
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Callaway et al. (1982) studied this question.
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