Self-consistent theory of polymerized membranes

Self-consistent theory of polymerized membranes.

We study D-dimensional polymerized membranes embedded in d dimensions using a selfconsistent screening approximation. It is exact for large d to order 1/d, for any d to order ǫ = 4−D and for d = D. For flat physical membranes (D = 2, d = 3) it predicts a roughness exponent ζ = 0.590. For phantom membranes at the crumpling transition the size exponent is ν = 0.732. It yields identical lower crit...

Self-avoiding Polymerized Membranes

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 ǫ-expansion for t...

Renormalization Theory for the Self-Avoiding Polymerized Membranes

We prove the renormalizability of the generalized Edwards model for self-avoiding polymerized membranes. This is done by use of a short distance multilocal operator product expansion, which extends the methods of local field theories to a large class of models with non-local singular interactions. This ensures the existence of scaling laws for crumpled self-avoiding membranes, and validates the...

Thermodynamical behavior of polymerized membranes

Anisotropic and Heterogeneous Polymerized Membranes

In these lectures I describe long scale properties of fluctuating polymerized membranes in the presence of network anisotropy and random heterogeneities. Amazingly, even infinitesimal amount of these seemingly innocuous but physically important ingredients in the membrane’s internal structure leads to a wealth of striking qualitatively new phenomena. Anisotropy leads to a “tubule” phase that is...