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 marked proximity with those obtained using nonperturbative techniques and reexpanded 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 compatible with known theoretical results and within the range of accepted numerical values.

arXiv comment(v2) Published in PRE Letter, some additions and minor modifications as per referee's comments, slight change in title as per editor's suggestion, no change in results. (v1) 10 pages

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• Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories
• Flat phase of quenched disordered membranes at three-loop order
• Disorder-driven transition to tubular phase in anisotropic two-dimensional materials
• Flat polymerized membranes at three-loop order