  We consider a general random walk loop soup which includes, or is related to,
several models of interest, such as the Spin O(N) model, the double dimer model
and the Bose gas. The analysis of this model is challenging because of the
presence of spatial interactions between the loops. For this model it is known
from Quitmann and Taggi (2022) that macroscopic loops occur in dimension three
and higher when the inverse temperature is large enough. Our first result is
that, on the $d$ dimensional lattice, the presence of repulsive interactions is
responsible for a shift of the critical inverse temperature, which is strictly
greater than $\frac{1}{2d}$, the critical value in the non interacting case.
Our second result is that a positive density of microscopic loops exists for
all values of the inverse temperature. This implies that, in the regime in
which macroscopic loops are present, microscopic and macroscopic loops coexist.
Moreover, we show that, even though the increase of the inverse temperature
leads to an increase of the total loop length, the density of microscopic loops
is uniformly bounded from above in the inverse temperature. Our last result is
confined to the special case in which the random walk loop soup is the one
associated to the Spin O(N) model with arbitrary integer values of $N \geq 2$
and states that, on $\mathbb{Z}^2$, the probability that two vertices are
connected by a loop decays at least polynomially fast with their distance.
