The tubular phase of self-avoiding anisotropic crystalline membranes

TL;DR

This paper investigates the properties of the tubular phase in self-avoiding anisotropic crystalline membranes, deriving critical exponents and analyzing fluctuation behaviors using renormalization group techniques.

Contribution

It introduces a comprehensive analysis of the tubular phase, including the derivation of critical exponents for the self-avoiding model using epsilon-expansion methods.

Findings

Exact solution for the non-self-avoiding limit.

Critical exponents nu=0.62 and zeta=0.80 estimated for the physical case.

Methodologies for extrapolating theoretical results to real-world parameters.

Abstract

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 epsilon-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 nu=0.62 for the Flory exponent and zeta=0.80 for the roughness exponent.