NONPERTURBATIVE RENORMALIZATION GROUP APPROACH TO POLYMERIZED MEMBRANES

Dominique Mouhanna (Personal webpage)

Polymerized membranes form a particularly rich domain of statistical physics where two-dimensional geometry and thermal fluctuations meet. This coexistence of geometry and possibly strong fluctuations has led to a lot of unexpected behaviors going from crumpled to flat, tubular or glassy phases. For several reasons that will be explained during these lectures the standard - perturbative - approaches are in particularly difficult position to correctly describe the critical behaviour of the various kinds of membranes known: isotropic or anisotropic, pure or disordered, with or without topological defects, etc. I will show in these lectures how a nonperturbative technique, known as the nonperturbative renormalization group, allows to correctly account for the physics of these systems in a large range of parameters - dimensions, temperature, coupling constants, etc.