Wrinkling transition in quenched disordered membranes at two loops

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.

arXiv comment8 pages, one figure, published version

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Cited by in corpus (6)

• Three-loop order approach to flat polymerized membranes
• Flat phase of quenched disordered membranes at three-loop order
• 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
• Perturbative renormalization and thermodynamics of quantum crystalline membranes