Phase Transitions and Gauge Artifacts in an Abelian Higgs Plus Singlet
  Model
  While the finite-temperature effective potential in a gauge theory is a
gauge-dependent quantity, in several instances a first-order phase transition
can be triggered by gauge-independent terms. A particularly interesting case
occurs when the potential barrier separating the broken and symmetric vacua of
a spontaneously broken symmetry is produced by tree-level terms in the
potential. Here, we study this scenario in a simple Abelian Higgs model, for
which the gauge-invariant potential is known, augmented with a singlet real
scalar. We analyze the possible symmetry breaking patterns in the model, and
illustrate in which cases gauge artifacts are expected to manifest themselves
most severely. We then show that gauge artifacts can be pronounced even in the
presence of a relatively large, tree-level singlet-Higgs cubic interaction.
When the transition is strongly first order, these artifacts, while present,
are more subtle than in the generic situation.
