Flat phase of quenched disordered membranes at three-loop order

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.

arXiv comment7 pages, 1 supplementary material file SM.m containing the 3-loop RG equations, published version

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Cited by in corpus (4)

• Disorder-driven transition to tubular phase in anisotropic two-dimensional materials
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• Renormalization group approach to the elastic properties of graphene bilayers