Numerical Observation of a Tubular Phase in Anisotropic Membranes

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 ${\nu }_F=0.305\mathrm{}\left(14\right)$ and $\zeta =0.895\mathrm{}\left(60\right)$, which are in reasonable agreement with the theoretical predictions of RT; ${\nu }_F=1\mathrm{}/4$ and $\zeta =1\mathrm{}$.