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(14) and zeta = 0.895(60), which are in reasonable agreement with the theoretical predictions of RT; nu(F) = 1/4 and zeta = 1.