论文标题
与最近的邻居诱捕诱捕自我避免的步行
Trapping in Self-Avoiding Walks with Nearest-Neighbor Attraction
论文作者
论文摘要
数十年来，自我避免随机步行的统计数据已用于对聚合物物理进行建模。一次在晶格上一次长大一步的自我避开步行最终将陷阱本身，这是在平均在平方晶格上71步的情况下发生的。在这里，我们考虑了最近邻居相互作用对不断增长的自我避免步行的影响，并研究了自我吸引对诱捕统计以及通过在Theta Point扩展和倒塌的步行之间的过渡而对捕获统计的效果。我们发现，诱捕长度随着最近的邻居接触能量的指数增长，但捕获长度的局部最小值对于弱自我吸引的步行。尽管存在与传统自我避免的步行相同的渐近行为是否具有相同的渐近行为是有争议的，但我们发现，theta点并不是在增长自我避免自我的步行的同一位置，并且持久性长度的收敛性更快地融合到了较小的价值。
The statistics of self-avoiding random walks have been used to model polymer physics for decades. A self-avoiding walk that grows one step at a time on a lattice will eventually trap itself, which occurs after an average of 71 steps on a square lattice. Here, we consider the effect of nearest-neighbor attractive interactions on the growing self-avoiding walk, and examine the effect that self-attraction has both on the statistics of trapping as well as on chain statistics through the transition between expanded and collapsed walks at the theta point. We find the trapping length increases exponentially with the nearest-neighbor contact energy, but that there is a local minimum in trapping length for weakly self-attractive walks. While it has been controversial whether growing self-avoiding walks have the same asymptotic behavior as traditional self-avoiding walks, we find that the theta point is not at the same location for growing self-avoiding walks, and that the persistence length converges much more rapidly to a smaller value.
