Flat phase of quenched disordered membranes at three-loop order
We study quenched disordered polymerized membranes in their flat phase by means of a three-loop perturbative analysis performed in dimension D =4 −ε . We derive the renormalization group equations at this order and solve them up to order ε3. Our results confirm those obtained by Coquand et al. within a nonperturbative approach [Phys. Rev. E 97, 030102(R) (2018), 10.1103/PhysRevE.97.030102] 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), 10.1103/PhysRevE.103.L031001], 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.
Physical Review E
- Pub Date:
- December 2022
- Condensed Matter - Disordered Systems and Neural Networks;
- High Energy Physics - Theory
- 7 pages, 1 supplementary material file SM.m containing the 3-loop RG equations, published version