Renormalization Group Flow of Hexatic Membranes

TL;DR

This paper studies the renormalization group flow of hexatic membranes, revealing a non-Gaussian fixed point where membranes become crinkled with fractal properties, using an invariant RG approach and effective field theory.

Contribution

It introduces a reparametrization invariant RG framework for hexatic membranes and analyzes the impact of long-range interactions on membrane rigidity parameters.

Findings

Identification of a non-Gaussian fixed point with crinkled membrane phase

Demonstration of long-range curvature interactions induced by coupled XY-model

Quantitative evaluation of surface tension and rigidity flow under RG

Abstract

We investigate hexatic membranes embedded in Euclidean D-dimensional space using a reparametrization invariant formulation combined with exact renormalization group (RG) equations. An XY-model coupled to a fluid membrane, when integrated out, induces long-range interactions between curvatures described by a Polyakov term in the effective action. We evaluate the contributions of this term to the running surface tension, bending and Gaussian rigidities in the approximation of vanishing disclination (vortex) fugacity. We find a non-Gaussian fixed-point where the membrane is crinkled and has a non-trivial fractal dimension.