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 $\varepsilon$ 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 $\mathrm{}(D=2,d=3\mathrm{})\mathrm{}$. Our most accurate estimates are $\nu =0.62\mathrm{}$ for the Flory exponent and $\zeta =0.80\mathrm{}$ for the roughness exponent.