论文标题
在高维托里上取消包装的两点功能
Unwrapped two-point functions on high-dimensional tori
论文作者
论文摘要
我们研究了ISING模型的未包装两点函数，自我避免的步行以及在具有周期性边界条件的高维晶格上进行随机循环的随机步行。尽管已经观察到这些模型的标准两点函数显示出异常的高原行为，但未包装的两点函数显示出显示标准的平均场行为。此外，我们认为，可以根据ZD上随机长度随机步行模型的标准两点函数来理解这些未包装的两点函数的渐近行为。针对后者的渐近行为得出了精确的描述。最后，我们考虑了Ising步行长度的自然概念，并在数值上表明，高维摩托车上的Ising和锯长长度显示出对完整图上的锯步长的相同通用行为。
We study unwrapped two-point functions for the Ising model, the self-avoiding walk and a random-length loop-erased random walk on high-dimensional lattices with periodic boundary conditions. While the standard two-point functions of these models have been observed to display an anomalous plateau behaviour, the unwrapped two-point functions are shown to display standard mean-field behaviour. Moreover, we argue that the asymptotic behaviour of these unwrapped two-point functions on the torus can be understood in terms of the standard two-point function of a random-length random walk model on Zd. A precise description is derived for the asymptotic behaviour of the latter. Finally, we consider a natural notion of the Ising walk length, and show numerically that the Ising and SAW walk lengths on high-dimensional tori show the same universal behaviour known for the SAW walk length on the complete graph.
