Flat phase of quantum polymerized membranes

First-order phase transitions in polymerized phantom membranes.

The crumpled-to-flat phase transition that occurs in D-dimensional polymerized phantom membranes embedded in a d-dimensional space is investigated nonperturbatively using a field expansion up to order 8 in powers of the order parameter. We get the critical dimension dcr(D) that separates a second-order region from a first-order one everywhere between D=4 and 2. Our approach strongly suggests th...

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...

Thermodynamical behavior of polymerized membranes

Flat glassy phases and wrinkling of polymerized membranes with long-range disorder.

We study polymerized membranes with long-range quenched internal disorder in the preferred metric and/or the extrinsic curvature characterized by disorder range exponents z ; z respectively. We nd several new at glassy phases stable at T > 0 in diierent regions of the z ; z plane. We calculate the z-dependent roughness exponents and amplitudes that characterize these new phases. When z , z exce...

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...