论文标题
近距离临界的两点功能和圆环高原，用于弱避免自我的步行
The near-critical two-point function and the torus plateau for weakly self-avoiding walk in high dimensions
论文作者
论文摘要
我们利用蕾丝扩展来研究整数晶格$ \ mathbb {z}^d $ in Dimensions $ d> 4 $，在关键点附近的两点函数的长距离衰减，并在关键点的附近，$ d> 4 $临界点处的平方根差异。作为一个应用程序，我们证明，在尺寸上的离散圆环上弱避免自我的步行的两点功能$ d> 4 $具有“高原”。我们还讨论了高原对分析圆环临界行为的重要性和后果。
We use the lace expansion to study the long-distance decay of the two-point function of weakly self-avoiding walk on the integer lattice $\mathbb{Z}^d$ in dimensions $d>4$, in the vicinity of the critical point, and prove an upper bound $|x|^{-(d-2)}\exp[-c|x|/ξ]$, where the correlation length $ξ$ has a square root divergence at the critical point. As an application, we prove that the two-point function for weakly self-avoiding walk on a discrete torus in dimensions $d>4$ has a "plateau." We also discuss the significance and consequences of the plateau for the analysis of critical behaviour on the torus.
