We investigate the flat phase of quenched disordered polymerized membranes by means of a two-loop, weak-coupling computation performed near their upper critical dimension $D_{uc}=4$, generalizing the one-loop computation of Morse et al. [D. C. Morse et al., Phys. Rev. A 45, R2151 (1992); D. C. Morse and T. C. Lubensky, Phys. Rev. A 46, 1751 (1992)]. Our work confirms the existence of the finite-temperature, finite-disorder wrinkling transition, which has been recently identified by Coquand et al. [O. Coquand et al., Phys. Rev. E 97, 030102(R) (2018)] using a nonperturbative renormalization group approach. We also point out ambiguities in the two-loop computation that prevent the exact identification of the properties of the novel fixed point associated with the wrinkling transition, which very likely requires a three-loop order approach.

中文翻译：

---

淬火无序膜在两个回路处的起皱转变

我们通过在其上临界尺寸附近进行的两环，弱耦合计算研究淬灭无序聚合膜的平坦相 $d_{üC}=4$，概括了Morse等人的单循环计算。[DC Morse等。，物理 修订版A 45，R2151（1992）; DC Morse和TC Lubensky，物理学。修订版A 46，1751（1992）]。我们的工作证实了有限温度，有限无序起皱过渡的存在，Coquand等人最近已经确定了这种过渡。[O. Coquand等。，物理 修订版E 97，030102（R）（2018）]使用非扰动重归一化组方法。我们还指出了两回路计算中的歧义，这妨碍了对与起皱过渡相关的新颖固定点的属性的准确识别，这很可能需要三回路顺序方法。