Abstract:Année de publication : 1996
Recent progresses in the understanding of the scaling behavior of self-avoiding flexible polymerized membranes (tethered manifolds) are reviewed (joint works with B. Duplantier and E. Guitter, and with K. Wiese). They rely on a new general renormalization group approach for a class of models with non-local singular interactions. This approach allows to prove the existence of a $\epsilon$-expansion for the scaling exponents, and validates the one loop results obtained by direct renormalization methods. Applications of the method to polymerized membranes at the tricritical $\Theta$-point are presented.