  These notes describe several loop soup models and their {\it universal
behaviour} in dimensions greater or equal to 3. These loop models represent
certain classical or quantum statistical mechanical systems. These systems
undergo phase transitions that are characterised by changes in the structures
of the loops. Namely, long-range order is equivalent to the occurrence of
macroscopic loops. There are many such loops, and the joint distribution of
their lengths is always given by a {\it Poisson-Dirichlet distribution}.
  This distribution concerns random partitions and it is not widely known in
statistical physics. We introduce it explicitly, and we explain that it is the
invariant measure of a mean-field split-merge process. It is relevant to
spatial models because the macroscopic loops are so intertwined that they
behave effectively in mean-field fashion. This heuristics can be made exact and
it allows to calculate the parameter of the Poisson-Dirichlet distribution. We
discuss consequences about symmetry breaking in certain quantum spin systems.
