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 isolated growing self-avoiding walks, and we 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 that 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.

中文翻译：

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避免与最近的景点进行自我规避的步行

自我规避的随机游走的统计数据已被用于模拟聚合物物理数十年。一次在格架上一次增长一个步的自我规避的行走最终将使自己陷入陷阱，而这在方形格上平均执行了71步之后才发生。在这里，我们考虑了最近邻吸引力交互对孤立的不断增长的自我规避步行的影响，并且我们研究了自我吸引对陷阱统计以及通过扩展步行和塌陷步行之间的转移的链统计的影响。在theta点。我们发现，诱捕长度随最近邻的接触能量呈指数增加，但是对于弱的自我吸引力步行，诱捕长度存在局部最小值。