A New Phase of Tethered Membranes: Tubules

TL;DR

This paper predicts a new 'tubule' phase in tethered membranes with anisotropy, characterized by a crumpled-in-one-direction and extended-in-another state, with universal properties and implications for membrane physics.

Contribution

It introduces and characterizes a novel 'tubule' phase in tethered membranes, extending the understanding of membrane phases beyond flat and crumpled states.

Findings

Existence of a new tubule phase between flat and crumpled phases.

Universal exponent for tubule thickness, a4=3/4, conjectured to be exact.

Analysis of elasticity and transition mechanisms into the tubule phase.

Abstract

We show that fluctuating tethered membranes with {\it 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 $R_G\sim L^{\nu_t}$ 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 $\nu_t=3/4$, which we conjecture is an exact result. We study the elasticity and fluctuations of the tubule state, and the transitions into it.