We investigate the asymptotic behaviour of multi-component links where the edges can be distributed among the components in all possible ways. Specifically we consider a link of k polygons on the simple cubic lattice. We prove two results about the exponential behaviour and use a Monte Carlo method to investigate how the value of the critical exponent depends on link type. One ring grows at the expense of the others while the remaining components act as one or more roots on the growing component, each root contributing 1 to the value of the critical exponent. Which component grows depends on which maximizes the entropy of the system

中文翻译：

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多分量链接多边形的渐近线

我们研究了多组件链接的渐近行为，其中边可以以所有可能的方式分布在组件之间。具体来说，我们考虑简单立方晶格上k 个多边形的链接。我们证明了关于指数行为的两个结果，并使用蒙特卡罗方法来研究临界指数的值如何取决于链接类型。一个环以其他环为代价增长，而其余分量作为生长分量的一个或多个根，每个根对临界指数的值贡献 1。哪个组件增长取决于哪个最大化系统的熵