Numerical Observation of a Tubular Phase in Anisotropic Membranes

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 $ν_F$ and the roughness exponent $ζ$. We find $ν_F=0.305(14)$ and $ζ=0.895(60)$, which are in reasonable agreement with the theoretical predictions of RT --- $ν_F=1/4$ and $ζ=1$.