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 νF and the roughness exponent ζ. We find νF0ex0ex=0ex0ex0.305(14) and ζ0ex0ex=0ex0ex0.895(60), which are in reasonable agreement with the theoretical predictions of RT; νF0ex0ex=0ex0ex1/4 and ζ0ex0ex=0ex0ex1.