A new phase of tethered membranes: Tubules

We show that fluctuating tethered membranes with any intrinsic anisotropy unavoidably exhibit a new phase between the previously predicted "flat" and "crumpled" phases, in high spatial dimensions d where the crumpled phase exists. In this new "tubule" phase, the membrane is crumpled in one direction but extended nearly straight in the other. Its average thickness is RG∼Lνt with L the intrinsic size of the membrane. This phase is more likely to persist down to d=3 than the crumpled phase. In Flory theory, the universal exponent νt=3/4, which we conjecture is an exact result. We study the elasticity and fluctuations of the tubule state, and the transitions into it. © 1995 The American Physical Society.