Effective models of membranes from symmetry breaking

TL;DR

This paper develops a unified formalism for membrane models using symmetry breaking, revealing how phase transitions induce long-range interactions and explaining intrinsic ripples in crystalline membranes.

Contribution

It introduces a method to derive membrane models via non-linear realizations of Euclidean symmetries, unifying various descriptions and identifying key order parameters.

Findings

Melting and loss of local order lead to long-range interactions.

The formalism explains intrinsic ripples in crystalline membranes.

Unified approach to membrane modeling from symmetry principles.

Abstract

We show how to obtain all the models of the continuous description of membranes by constructing the appropriate non-linear realizations of the Euclidean symmetries of the embedding. The procedure has the advantage of giving a unified formalism with which the models are generated and highlights the relevant order parameters in each phase. We use our findings to investigate a fluid description of both tethered and hexatic membranes, showing that both the melting and the loss of local order induce long range interactions in the high temperature fluid phase. The results can be used to understand the appearance of intrinsic ripples in crystalline membranes in a thermal bath.