  Proliferation of defects is a mechanism that allows for topological phase
transitions. Such a phase transition is found in two dimensions for the
XY-model, which lies in the Berezinskii-Kosterlitz-Thouless (BKT) universality
class. The transition point can be found using renormalization group analysis.
We apply renormalization group arguments to determine the nature of BKT
transitions for the three-dimensional plaquette-dimer model, which is a model
that exhibits fractonic mobility constraints. We show that an important part of
this analysis demands a modified dimensional analysis that changes the
interpretation of scaling dimensions upon coarse-graining. Using this modified
dimensional analysis we compute the beta functions of the model and predict a
finite critical value above which the fractonic phase melts, proliferating
dipoles. Importantly, the transition point is found through a renormalization
group analysis that accounts for the phenomenon of UV/IR mixing, characteristic
of fractonic models.
