| Abstract: | A "loop soup" is an ensemble of interlaced loops of various shapes
and lengths. Several models in equilibrium statistical mechanics can
be described by loop soups, such as the dilute Bose gas and the
classical and quantum Heisenberg models.
A universal feature of loop soups in 3D is the existence of phases
with loops of macroscopic lengths. The joint distribution of these
lengths is always given by a Poisson-Dirichlet distribution. I will
review these ideas and describe some consequences about the
nature of symmetry breaking in certain quantum spin systems.
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