Flat phase of polymerized membranes at two-loop order

Coquand, Olivier; Mouhanna, D.; Teber, S.

doi:10.1103/physreve.101.062104

Cited by 26 publications

(57 citation statements)

References 71 publications

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“…In that respect, an essential feature of the novel fixed point P c found in [41] is that its coordinates near D uc = 4 differ only from those of the vanishing-temperature fixed point P 5 by terms of order 2 , with = 4 − D, strongly suggesting that P c could also be identified within a perturbative expansion up to this order. This is the reason why, in this Letter, we investigate quenched disordered membranes at two loops in the vicinity of the upper critical dimension, extending both the one-loop computation of Morse et al performed 30 years ago [24,25] at the next order and the recent two-loop computation of Coquand et al [44] (see also [45]) on disorder-free membranes to the disordered case. We derive the RG equations, analyze them, and provide the critical quantities, notably the anomalous dimension η, at order 2 .…”

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confidence: 79%

“…At two-loop order, we recover the disorder-free fixed point P 4 whose coordinates and anomalous dimension have been given in [44]. Using the variables relevant to study the vanishing temperature, we also identify a fixed point with μ = 0 that coincides with the fixed point P 5 found at one-loop order.…”

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confidence: 90%

“…Renormalization group equations and fixed points. As in the disorder-free [44,46,47] case, Ward identities associated with a partial rotation invariance ensure the renormalizability of the theory. Also, only the renormalizations of phonon and flexural mode propagators are required.…”

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confidence: 99%

“…Also, only the renormalizations of phonon and flexural mode propagators are required. As in [44], we have treated the massless theory using the modified minimal subtraction scheme and used standard techniques for computing massless Feynman diagram calculations; see, e.g., [48]. As usual, one defines dimensionless coupling constants…”

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confidence: 99%

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Wrinkling transition in quenched disordered membranes at two loops

Coquand

Mouhanna

2021

Phys. Rev. E

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We investigate 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 et al. [D. C. Morse et al., Phys. Rev. A 45, R2151 (1992); D. C. Morse and T. C. Lubensky, 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. [O. Coquand et al., Phys. Rev. E 97, 030102(R) ( 2018)] using a nonperturbative renormalization group approach. We also point 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.

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confidence: 79%

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confidence: 90%

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confidence: 99%

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confidence: 99%

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Wrinkling transition in quenched disordered membranes at two loops

Coquand

Mouhanna

2021

Phys. Rev. E

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“…As a result of strong nonlinear coupling between bending and shear deformations, thermal fluctuations in the flat phase present anomalous scale invariance characterized by universal noninteger exponents. In the long-wavelength limit, the scale-dependent effective compression and shear moduli are driven to zero as power laws of the wave vector q, while the effective bending rigidity diverges as κ (q) ≈ q −η [6][7][8]10,11,17,18]. This anomalous infrared behavior sets in at a characteristic Ginzburg scale q * ≈ 3TY/(16πκ 2 ), where κ, Y , and T are, respectively, the bare bending rigidity, Young modulus, and temperature [3,19].…”

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confidence: 99%

Thermal ripples in bilayer graphene

Mauri¹,

Soriano²,

Katsnelson³

2020

Phys. Rev. B

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We study thermal fluctuations of freestanding bilayer graphene subject to vanishing external tension. Within a phenomenological theory, the system is described as a stack of two continuum crystalline membranes, characterized by finite elastic moduli and a nonzero bending rigidity. A nonlinear rotationally invariant model guided by elasticity theory is developed to describe interlayer interactions. After neglection of in-plane phonon nonlinearities and anharmonic interactions involving interlayer shear and compression modes, an effective theory for soft flexural fluctuations of the bilayer is constructed. The resulting model, neglecting anisotropic interactions, has the same form of a well-known effective theory for out-of-plane fluctuations in a single-layer membrane, but with a strongly wave-vector-dependent bare bending rigidity. Focusing on AB-stacked bilayer graphene, parameters governing interlayer interactions in the theory are derived by first-principles calculations. Statistical-mechanical properties of interacting flexural fluctuations are then calculated by a numerical iterative solution of field-theory integral equations within the self-consistent screening approximation. The bare bending rigidity in the considered model exhibits a crossover between a long-wavelength regime governed by in-plane elastic stress and a short wavelength region controlled by monolayer curvature stiffness. Interactions between flexural fluctuations drive a further crossover between a harmonic and a strong-coupling regime, characterized by anomalous scale invariance. The overlap and interplay between these two crossover behaviors is analyzed at varying temperatures.

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Scale and conformal invariance in higher derivative shift symmetric theories

Safari

Stergiou

Vacca

et al. 2022

J. High Energ. Phys.

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The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical dimensions and studied at the leading non trivial order in perturbation theory. For two infinite families, one with quartic and one with cubic interactions, beta functions, criticality conditions and universal anomalous dimensions are computed. At the order considered, the cubic theories enjoy a one loop non renormalization of the vertex, so that the beta function depends non trivially only on the anomalous dimension. The trace of the energy momentum tensor is also investigated and it is shown that these two families of QFTs are conformally invariant at the fixed point of the RG flow.

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Flat phase of polymerized membranes at two-loop order

Cited by 26 publications

References 71 publications

Wrinkling transition in quenched disordered membranes at two loops

Wrinkling transition in quenched disordered membranes at two loops

Thermal ripples in bilayer graphene

Scale and conformal invariance in higher derivative shift symmetric theories

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