# A three-loop order approach to flat polymerized membranes

Abstract : We derive the three-loop order renormalization group equations that describe the flat phase of polymerized membranes within the modified minimal subtraction scheme, following the pioneering one-loop order computation of Aronovitz and Lubensky [Phys. Rev. Lett. 60, 2634 (1988)] and the recent two-loop order one of Coquand, Mouhanna and Teber [Phys. Rev. E 101, 062104 (2020)]. We analyze the fixed points of these equations and compute the associated field anomalous dimension $\eta$ at three-loop order. Our results display a striking proximity with those obtained using nonperturbative techniques and re-expanded in powers of $\epsilon=4-D$. Moreover, the three-loop order value that we get for $\eta$ at the stable fixed point, $\eta=0.8872$, in $D=2$, is in quantitative agreement with known theoretical and numerical values.
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https://hal.archives-ouvertes.fr/hal-03354063
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Submitted on : Friday, September 24, 2021 - 3:45:07 PM
Last modification on : Saturday, September 25, 2021 - 3:30:44 AM

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### Citation

S. Metayer, D. Mouhanna, S. Teber. A three-loop order approach to flat polymerized membranes. 2021. ⟨hal-03354063⟩

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