The winding angle of planar self-avoiding walks
The winding angle of planar self-avoiding walks
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平面自避走道的缠绕角度
DOI：
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
S. Redner
中科院分区：
文献类型：
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作者：
M. Fisher;V. Privman;S. Redner
本文提出了一个关于平面格点上N步自回避行走的缠绕角ON的渐近统计行为的问题。精确的系列扩展数据的正方形晶格高达N = 21的报告。这些数据和蒙特卡罗估计高达N G 170步，很好地拟合对数增长律（06）。比率（@，，）/（Oh）* 似乎接近2.9至3.2的极限，这接近高斯值3。启发式尺度参数与简单的对数增长一致（也阐明了自由布朗运动严格已知的对数行为）。
The problem of understanding the asymptotic statistical behaviour of the winding angle, ON, of a self-avoiding walk of N steps on a planar lattice is posed. Exact series expansion data for the square lattice up to N = 21 are reported. These data and Monte Carlo estimates up to N G 170 steps are fitted well by a logarithmic growth law for (06). The ratio (@,,)/(Oh)* appears to approach a limit of 2.9 to 3.2, which is close to the Gaussian value, 3. Heuristic scaling arguments are consistent with simple logarithmic growth (and also illuminate the logarithmic behaviour known rigorously for free Brownian motion).