Self-Avoiding Polymerized Membranes

Recent progresses in the understanding of the scaling behavior of self-avoiding flexible polymerized membranes (tethered manifolds) are reviewed. 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.