Tubular phase of self-avoiding anisotropic crystalline membranes

We analyze the tubular phase of self-avoiding anisotropic crystalline membranes. A careful analysis using renormalization group arguments together with symmetry requirements motivates the simplest form of the large-distance free energy describing fluctuations of tubular configurations. The non-self-avoiding limit of the model is shown to be exactly solvable. For the full self-avoiding model we compute the critical exponents using an ɛ expansion about the upper critical embedding dimension for general internal dimension D and embedding dimension d. We then exhibit various methods for reliably extrapolating to the physical point (D=2,d=3). Our most accurate estimates are ν=0.62 for the Flory exponent and ζ=0.80 for the roughness exponent.