Self-Avoiding Polymerized Membranes

TL;DR

This paper reviews recent advances in understanding the scaling behavior of self-avoiding polymerized membranes using a novel renormalization group approach, confirming previous results and exploring applications at the tricritical Theta-point.

Contribution

It introduces a new renormalization group method for non-local interactions, validating and extending prior one-loop results for polymerized membranes.

Findings

Existence of an epsilon-expansion for scaling exponents

Validation of one-loop renormalization results

Application to membranes at the tricritical Theta-point

Abstract

Recent progresses in the understanding of the scaling behavior of self-avoiding flexible polymerized membranes (tethered manifolds) are reviewed. They rely on a new general renormalization group approach for a class of models with non-local singular interactions. This approach allows to prove the existence of a epsilon-expansion for the scaling exponents, and validates the one loop results obtained by direct renormalization methods. Applications of the method to polymerized membranes at the tricritical Theta-point are presented.