Large-scale Monte Carlo simulations are employed to study phase transitions
in the three-dimensional compact abelian Higgs model in adjoint representations
of the matter field, labelled by an integer q, for q=2,3,4,5. We also study
various limiting cases of the model, such as the Zq lattice gauge theory,
dual to the 3DZq spin model, and the 3DXY spin model which is dual to the
Zq lattice gauge theory in the limit q→∞. We have computed the
first, second, and third moments of the action to locate the phase transition
of the model in the parameter space (β,κ), where β is the
coupling constant of the matter term, and κ is the coupling constant of
the gauge term. We have found that for q=3, the three-dimensional compact
abelian Higgs model has a phase-transition line βc(κ) which
is first order for κ below a finite {\it tricritical} value
κtri, and second order above. We have found that the
β=∞ first order phase transition persists for finite β and
joins the second order phase transition at a tricritical point
(βtri,κtri)=(1.23±0.03,1.73±0.03). For
all other integer q≥2 we have considered, the entire phase transition
line βc(κ) is critical.Comment: 17 pages, 12 figures (new Fig. 2), new Section IVB, updated
references, submitted to Physical Review