Most common critical systems in condensed matter and statistical
mechanics are associated with a discrete set of critical exponents,
which can be traced back to the compact nature of the corresponding
field theories. There are however many noticeable cases where
continuous spectra of exponents are observed, a poreminent example
being that of the Integer Quantum Hall Effect. Whereas in the compact
case a lot of insight is usually gained by turning to (integrable)
regularizations such as lattice models or spin chains, a connection
between non compact field theories and the world of integrable spin
chains has for long been lacking. In this talk, we will see that there
actually many 'physical' spin chains or statistical lattice models
corresponding to non compact conformal field theories. There are many
consequences to this observation, and I will present applications of
our results to polymer physics as well as to the construction of
integrable truncations of the IQHE plateau transitons.
This is based on joint work with Jesper Jacobsen (LPTENS, Paris) and
Hubert Saleur (IPhT, Saclay).
