标题： 场论方法研究平坦聚合物膜 显示英文标题

标题： Field-theory approach to flat polymerized membranes

摘要： 我们回顾了场论重正化群方法在平面聚合物膜临界性质中的应用。 我们从柔性有效模型的介绍开始，该模型完全用横向（弯曲）场及其非局域相互作用来表示。 随后，我们在维数正则化方案内详细介绍了模型重正化群函数的完整三圈计算。 这种方法允许我们考虑一般情况下的 $d$-维膜嵌入到 $D$-维空间中的情形。 集中讨论三维空间 $(D = 3)$中二维膜 $(d = 2)$的临界平坦相，我们分析了相应的流图，并推导出异常刚度。 后者控制着理论中其他所有临界指数，例如粗糙度指数和弹性常数的标度。 此外，还提供了最先进的四圈结果以及关于微扰级数结构的讨论，并与其他方法进行了比较。 显示英文摘要

摘要： We review the field-theoretic renormalization-group approach to critical properties of flat polymerized membranes. We start with a presentation of the flexural effective model that is entirely expressed in terms of a transverse (flexural) field with non-local interactions. We then provide a detailed account of the full three-loop computations of the renormalization-group functions of the model within the dimensional regularization scheme. The latter allows us to consider the general case of a $d$-dimensional membrane embedded in $D$-dimensional space. Focusing on the critical flat phase of two-dimensional membranes $(d = 2)$ in three-dimensional space $(D = 3)$, we analyse the corresponding flow diagram and present the derivation of the anomalous stiffness. The latter controls all the other critical exponents of the theory such as the roughness exponent and the scaling of the elastic constants. State-of-the-art four-loop results as well as discussions on the structure of the perturbative series and comparison with other approaches are also provided.