Effects of Self-Avoidance on the Tubular Phase of Anisotropic Membranes

TL;DR

This paper investigates the effects of self-avoidance on the tubular phase of anisotropic membranes, deriving scaling relations and critical exponents through renormalization group analysis and perturbative methods.

Contribution

It introduces a renormalizable model for self-avoiding anisotropic membranes and computes critical exponents using epsilon-expansion techniques.

Findings

Derived general scaling relations for the model's exponents

Reproduced Gaussian, Flory, and variational results through renormalization choices

Calculated critical exponents to first order in epsilon-expansion

Abstract

We study the tubular phase of self-avoiding anisotropic membranes. We discuss the renormalizability of the model Hamiltonian describing this phase and derive from a renormalization group equation some general scaling relations for the exponents of the model. We show how particular choices of renormalization factors reproduce the Gaussian result, the Flory theory and the Gaussian Variational treatment of the problem. We then study the perturbative renormalization to one loop in the self-avoiding parameter using dimensional regularization and an epsilon-expansion about the upper critical dimension, and determine the critical exponents to first order in epsilon.