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
.