Random linking of lattice polygons
Random linking of lattice polygons
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格子多边形的随机连接
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
S. Whittington
中科院分区：
文献类型：
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作者：
E. Orlandini;E. J. J. Rensburg;M. C. Tesi;S. Whittington
研究了简单立方格子上多边形的连通概率。特别地，我们考虑两个各有n条边的多边形，限制在一个边长为L的立方体内，并求出连接概率作为n和L的函数。我们还考虑了其他情况，其中限制多边形间的距离不能太远，但不一定限制在一个立方体内。我们证明了几个严格的结果，并用蒙特卡罗方法解决了一些我们不能严格回答的问题。一个有趣的特征是链接概率是L/Nv的函数，其中v是表征多边形旋转半径的指数。
We study the linking probability of polygons on the simple cubic lattice. In particular, we consider two polygons each having n edges, confined to a cube of side L, and ask for the linking probability as a function of n and L. We also consider other situations in which the polygons are restricted to be not too far apart, but not necessarily confined to a cube. We prove several rigorous results, and use Monte Carlo methods to address some questions which we are unable to answer rigorously. An interesting feature is that the linking probability is a function of L/nv, where v is the exponent characterizing the radius of gyration of a polygon.