Fluctuating Membranes with Tilt Order

TL;DR

This paper investigates how thermal fluctuations influence membranes with nematic tilt order, revealing they belong to the same universality class as hexatic membranes and demonstrating the benefits of conformal gauge for analysis.

Contribution

It introduces a simplified model of nematic membranes, showing their equivalence to hexatic membranes and highlighting the advantages of conformal gauge in theoretical calculations.

Findings

Nematic membranes are in the same universality class as hexatic membranes.

Couplings distinguishing nematic from hexatic order are marginally irrelevant.

Conformal gauge simplifies the analysis of fluctuating membranes.

Abstract

Thermal fluctuations are important for amphiphilic bilayer membranes since typical bending stiffnesses can be a few $k_B T$. The rod-like constituent molecules are generically tilted with respect to the local normal for packing reasons. We study the effects of fluctuations on membranes with nematic order, a simplified idealization with the same novel features as realistic tilt order. We find that nematic membranes lie in the same universality class as hexatic membranes, {\it i.e.} the couplings that distinguish nematic from hexatic order are marginally irrelevant. Our calculation also illustrates the advantages of conformal gauge, which brings great conceptual and technical simplifications compared to the more popular Monge gauge.