  The double dimer model is defined as the superposition of two independent
uniformly distributed dimer covers of a graph. Its configurations can be viewed
as disjoint collections of self-avoiding loops. Our first result is that in
$\mathbb{Z}^d$, $d>2$, the loops in the double dimer model are macroscopic.
These are shown to behave qualitatively differently than in two dimensions. In
particular, we show that, given two distant points of a large box, with
uniformly positive probability there exists a loop visiting both points. Our
second result involves the monomer double-dimer model, namely the double-dimer
model in the presence of a density of monomers. These are vertices which are
not allowed to be touched by any loop. This model depends on a parameter, the
monomer activity, which controls the density of monomers. It is known from Betz
and Taggi (2019) and Taggi (2021) that a finite critical threshold of the
monomer activity exists, below which a self-avoiding walk forced through the
system is macroscopic. Our paper shows that, when $d >2$, such a critical
threshold is strictly positive. In other words, the self-avoiding walk is
macroscopic even in the presence of a positive density of monomers.
