  We study a phase transition in a 3D lattice gauge theory, a "coarse-grained"
version of a classical dimer model. Duality arguments indicate that the dimer
lattice theory should be dual to a XY model coupled to a gauge field with
geometric frustration. The transition between a Coulomb phase with dipolar
correlations and a long range ordered columnar phase is understood in terms of
a Higgs mechanism. Monte Carlo simulations of the dual model indicate a
continuous transition with exponents close but apparently different from those
of the 3d XY model. The continuous nature of the transition is confirmed by a
flowgram analysis.
