标题： 分形上的线性和支化聚合物 显示英文标题

标题： Linear and branched polymers on fractals

摘要： 这是一篇关于确定性有限分支分形上线性聚合物的教育性综述。 对于这些分形，可以使用实空间重正化群技术精确地确定临界性质。 我们展示如何用这种方法来确定不同分形上自避行走的临界指数。 研究了当底层分形的分数维接近 2 时，$n$-单纯形点阵上的临界指数在大$n$极限下的行为。 我们研究了分数维刚刚低于 2 的情况下自避行走的行为。 然后我们考虑带有吸引相互作用的线性聚合物的情况，在某些分形上会导致塌缩转变。 分形还提供了一个场景，可以在其中解析地研究线性链在有吸引力的基底表面附近的吸附以及两个相互作用链的拉链-解链转变。 我们还简要讨论了分形上支化聚合物的临界性质。 显示英文摘要

摘要： This is a pedagogical review of the subject of linear polymers on deterministic finitely ramified fractals. For these, one can determine the critical properties exactly by real-space renormalization group technique. We show how this is used to determine the critical exponents of self-avoiding walks on different fractals. The behavior of critical exponents for the $n$-simplex lattice in the limit of large $n$ is determined. We study self-avoiding walks when the fractal dimension of the underlying lattice is just below 2. We then consider the case of linear polymers with attractive interactions, which on some fractals leads to a collapse transition. The fractals also provide a setting where the adsorption of a linear chain near on attractive substrate surface and the zipping-unzipping transition of two mutually interacting chains can be studied analytically. We also discuss briefly the critical properties of branched polymers on fractals.