Elasticity, Shape Fluctuations and Phase Transitions in the New Tubule Phase of Anisotropic Tethered Membranes

TL;DR

This paper investigates the shape, elasticity, and phase transitions of the tubule phase in anisotropic tethered membranes, providing scaling laws, theoretical predictions, and simulation comparisons for its properties and transitions.

Contribution

It offers the first detailed scaling theory and renormalization group analysis of the tubule phase and its phase transitions in anisotropic membranes, including effects of self-avoidance.

Findings

Predicted shape exponents for phantom membranes match simulations.

Self-avoidance alters shape exponents and suppresses undulations.

Derived scaling laws for tubule shape and elasticity.

Abstract

We study the shape, elasticity and fluctuations of the recently predicted (cond-mat/9510172) and subsequently observed (in numerical simulations) (cond-mat/9705059) tubule phase of anisotropic membranes, as well as the phase transitions into and out of it. This novel phase lies between the previously predicted flat and crumpled phases, both in temperature and in its physical properties: it is crumpled in one direction, and extended in the other. Its shape and elastic properties are characterized by a radius of gyration exponent $\nu$ and an anisotropy exponent $z$. We derive scaling laws for the radius of gyration $R_G(L_\perp,L_y)$ (i.e. the average thickness) of the tubule about a spontaneously selected straight axis and for the tubule undulations $h_{rms}(L_\perp,L_y)$ transverse to its average extension. For phantom (i.e. non-self-avoiding) membranes, we predict $\nu=1/4$, $z=1/2$ and $\eta_\kappa=0$, exactly, in excellent agreement with simulations. For membranes embedded in the space of dimension $d<11$, self-avoidance greatly swells the tubule and suppresses its wild transverse undulations, changing its shape exponents $\nu$ and $z$. We give detailed scaling results for the shape of the tubule of an arbitrary aspect ratio and compute a variety of correlation functions, as well as the anomalous elasticity of the tubules. Finally we present a scaling theory for the shape of the membrane and its specific heat near the continuous transitions into and out of the tubule phase and perform detailed renormalization group calculations for the crumpled-to-tubule transition for phantom membranes.