Abstract
 
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 prominent 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).