Numerical Observation of a Tubular Phase in Anisotropic Membranes

TL;DR

This paper provides the first numerical evidence for a tubular phase in anisotropic tethered membranes, confirming theoretical predictions through phase transition analysis and measurement of critical exponents.

Contribution

It introduces a numerical model demonstrating the existence of a tubular phase in anisotropic membranes, validating prior theoretical predictions.

Findings

Identification of two phase transitions: flat-to-tubular and tubular-to-crumpled.

Measured Flory exponent $ u_F=0.305(14)$ and roughness exponent $0.895(60)$ in the tubular phase.

Results are in reasonable agreement with theoretical predictions of RT.

Abstract

We provide the first numerical evidence for the existence of a tubular phase, predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes without self-avoidance. Incorporating anisotropy into the bending rigidity of a simple model of a tethered membrane with free boundary conditions, we show that the model indeed has two phase transitions corresponding to the flat-to-tubular and tubular-to-crumpled transitions. For the tubular phase we measure the Flory exponent $\nu_F$ and the roughness exponent $\zeta$. We find $\nu_F=0.305(14)$ and $\zeta=0.895(60)$, which are in reasonable agreement with the theoretical predictions of RT --- $\nu_F=1/4$ and $\zeta=1$.