Wrinkling transition in quenched disordered membranes at two loops

TL;DR

This paper analyzes the flat phase of quenched disordered membranes using a two-loop perturbative approach near the upper critical dimension, confirming a finite-temperature wrinkling transition and discussing computational ambiguities.

Contribution

It extends previous one-loop studies by performing a two-loop analysis, confirming the wrinkling transition, and highlighting the need for higher-order calculations.

Findings

Confirmed the existence of a finite-temperature, finite-disorder wrinkling transition.

Identified ambiguities in two-loop computations affecting fixed point properties.

Suggested that a three-loop approach may be necessary for precise characterization.

Abstract

One investigates the flat phase of quenched disordered polymerized membranes by means of a two-loop, weak-coupling computation performed near their upper critical dimension $D_{uc} = 4$, generalizing the one-loop computation of Morse, Lubensky and Grest [Phys. Rev. A 45, R2151 (1992), Phys. Rev. A 46, 1751 (1992)]. Our work confirms the existence of the finite-temperature, finite-disorder, wrinkling transition, which has been recently identified by Coquand et al. [Phys. Rev E 97, 030102 (2018)] using a nonperturbative renormalization group approach. One also points out ambiguities in the two-loop computation that prevent the exact identification of the properties of the novel fixed point associated with the wrinkling transition, which very likely requires a three-loop order approach.