We investigate the flat phase of quantum polymerized phantom membranes by means of a nonperturbative renormalization group approach. We first implement this formalism for general quantum polymerized membranes and derive the flow equations that encompass both quantum and thermal fluctuations. We then deduce and analyze the flow equations relevant to study the flat phase and discuss their salient features : quantum to classical crossover and, in each of these regimes, strong to weak coupling crossover. We finally illustrate these features in the context of free standing graphene physics.
In this conference report, we present a recent field theoretic renormalization group analysis of flat polymerized membranes at three-loop order by the present authors [Phys. Rev. E 105, L012603 (2022)].
We calculate four-loop order corrections to the critical exponent $η$ in the two-field model of flat phase membranes. Obtained results show better agreement with the other calculation methods and confirm the validity of the perturbative approach to the considered problem.
We investigate two complementary field-theoretical models describing the flat phase of polymerized - phantom - membranes by means of a two-loop, weak-coupling, perturbative approach performed near the upper critical dimension $D_{uc}=4$, extending the one-loop computation of Aronovitz and Lubensky [Phys. Rev. Lett. 60, 2634 (1988)]. We derive the renormalization group equations within the modified minimal substraction scheme, then analyze the corrections coming from two-loop with a particular attention paid to the anomalous dimension and the asymptotic infrared properties of the renormalizatio…
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 $η$ at three-loop order. Our results display a marked proximity with those obtained using nonperturbative techniques and r…
Crystalline membranes are one of the rare examples of bidimensional systems in which long-range order can stabilise an ordered phase in the thermodynamic limit. By a careful analysis of the Goldstone modes counting, we propose a symmetry breaking mechanism associated with the generation of the flat phase and show how it highlights the crucial role played by the crystalline lattice in the establishment of long-range order in these objects. Comparison with other symmetry breaking mechanisms in membrane physics is also used to unveil the links between symmetry breaking patterns and the physical p…
Activity-induced emergent flatness, instabilities and pattern formation in fluid membranes
Theoretical Physics Division, Saha Institute of Nuclear Physics, a CI of Homi Bhabha National Institute（萨哈核物理研究所理论物理部，霍米·巴巴国立大学附属机构）；Center for Biophysics & Department of Theoretical Physics, Saarland University（萨尔兰大学生物物理中心与理论物理系）
Whether live cell membranes show miscibility phase transitions (MPTs), and if so, how they fluctuate near the transitions remain outstanding unresolved issues in physics and biology alike. Motivated by these questions we construct a generic hydrodynamic theory for lipid membranes {that are active, due for instance, to the molecular motors in the surrounding cytoskeleton, or active protein components in the membrane itself}. We use this to uncover a direct correspondence between membrane fluctuations and MPTs. Several testable predictions are made: (i) generic {\em active stiffening} with orien…
