  One of the simplest examples of a PT-symmetric quantum system is the scaling
Yang-Lee model, a quantum field theory with cubic interaction and purely
imaginary coupling. We give a historical review of some facts about this model
in d <= 2 dimensions, from its original definition in connection with phase
transitions in the Ising model and its relevance to polymer physics, to the
role it has played in studies of integrable quantum field theory and of
PT-symmetric quantum mechanics. We also discuss some more general results on
PT-symmetric quantum mechanics and the ODE/IM correspondence, and mention
applications to magnetic systems and cold atom physics.
