  We study critical behavior in the classical cubic dimer model (CDM) in the
presence of a finite density of monomers. With attractive interactions between
parallel dimers, the monomer-free CDM exhibits an unconventional transition
from a Coulomb phase to a dimer crystal. Monomers acts as charges (or
monopoles) in the Coulomb phase and, at nonzero density, lead to a standard
Landau-type transition. We use large-scale Monte Carlo simulations to study the
system in the neighborhood of the critical point, and find results in agreement
with detailed predictions of scaling theory. Going beyond previous studies of
the transition in the absence of monomers, we explicitly confirm the
distinction between conventional and unconventional criticality, and
quantitatively demonstrate the crossover between the two. Our results also
provide additional evidence for the theoretical claim that the transition in
the CDM belongs in the same universality class as the deconfined quantum
critical point in the SU(2) JQ model.
