Flat phase of quenched disordered membranes at three-loop order

TL;DR

This paper performs a three-loop perturbative analysis of quenched disordered membranes in their flat phase, confirming and refining previous nonperturbative and two-loop results on phase transitions and scaling behavior.

Contribution

It provides a detailed three-loop renormalization group analysis of disordered membranes, improving understanding of their phase transitions and scaling properties.

Findings

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

Computed anomalous dimensions consistent with nonperturbative predictions.

Corrected previous two-loop results for the scaling behavior.

Abstract

We study quenched disordered polymerized membranes in their flat phase by means of a three-loop perturbative analysis performed in dimension $D = 4-\epsilon$. We derive the renormalization group equations at this order and solve them up to order $\epsilon^3$. Our results confirm those obtained by Coquand et al. within a nonperturbative approach [Phys. Rev. E 97, 030102(R) (2018)] predicting a finite-temperature, finite-disorder wrinkling transition and those obtained by Coquand and Mouhanna within a recent two-loop order approach [Phys. Rev. E 103, L031001 (2021)], while correcting some of the results obtained in this last reference. We compute the anomalous dimensions that characterize the scaling behavior at the various fixed points of the renormalization group flow diagram. They appear to be in strong agreement with those predicted within the nonperturbative context.