  A review is given on the recently proposed two dimensional axion model (O(3)
sigma-model with a dynamical Hopf-term) and the T-duality relating it to the
SU(2)xU(1) symmetric anisotropic sigma-model. Strong evidence is presented for
the correctness of the proposed S-matrix for both models comparing perturbative
and Thermodynamical Bethe Ansatz calculations for different types of free
energies. This also provides a very stringent test of the validity of T-duality
transformation at the quantum level. The quantum non-integrability of the O(3)
sigma-model with a non-dynamical Hopf-term, in contradistinction to the axion
model, is illustrated by calculating the 2-->3 particle production amplitude to
lowest order.
