Metayer S, Mouhanna D, Teber S
Sorbonne Université, CNRS, Laboratoire de Physique Théorique et Hautes Energies, LPTHE, 75005 Paris, France.
Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensé, 75005 Paris, France.
Phys Rev E. 2022 Jan;105(1):L012603. doi: 10.1103/PhysRevE.105.L012603.
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)10.1103/PhysRevLett.60.2634] and the recent two-loop order one of Coquand, Mouhanna, and Teber [Phys. Rev. E 101, 062104 (2020)2470-004510.1103/PhysRevE.101.062104]. 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 reexpanded in powers of ε=4-D. Moreover, the three-loop order value that we get for η at the stable fixed point, η=0.8872, in D=2, is compatible with known theoretical results and within the range of accepted numerical values.
我们推导了在修正的最小减法方案中描述聚合膜平坦相的三圈阶重整化群方程，这是在阿罗诺维茨和卢本斯基的开创性一圈阶计算[《物理评论快报》60, 2634 (1988)10.1103/PhysRevLett.60.2634]以及科昆德、穆哈纳和特伯最近的两圈阶计算[《物理评论E》101, 062104 (2020)2470 - 004510.1103/PhysRevE.101.062104]之后进行的。我们分析了这些方程的不动点，并计算了三圈阶相关的场反常维度η。我们的结果与使用非微扰技术并按ε = 4 - D的幂次重新展开得到的结果显示出显著的接近性。此外，我们在D = 2时稳定不动点处得到的η的三圈阶值，η = 0.8872，与已知的理论结果兼容，且在公认的数值范围内。
