论文标题
Bose气体，自旋O（N）和相关模型中的宏观环路
Macroscopic loops in the Bose gas, Spin O(N) and related models
论文作者
论文摘要
我们考虑了一个一般的交互随机循环系统，其中包括几种感兴趣的模型，例如自旋O（n）模型，随机晶格排列，在离散空间中和循环O（n）模型中相互作用的bose气体的版本。我们考虑$ \ Mathbb {z}^d $，$ d \ geq 3 $中的系统，并证明其长度与系统体积成正比的宏观循环发生。更确切地说，我们通过有限盒近似$ \ mathbb {z}^d $，并且给定距离与盒子直径成正比的两个顶点，我们证明观察循环访问的循环的概率是均匀的。我们的结果在对相互作用潜力的一般假设下，可能具有界定或无限的支持或引入硬核约束。
We consider a general system of interacting random loops which includes several models of interest, such as the Spin O(N) model, random lattice permutations, a version of the interacting Bose gas in discrete space and of the loop O(N) model. We consider the system in $\mathbb{Z}^d$, $d \geq 3$, and prove the occurrence of macroscopic loops whose length is proportional to the volume of the system. More precisely, we approximate $\mathbb{Z}^d$ by finite boxes and, given any two vertices whose distance is proportional to the diameter of the box, we prove that the probability of observing a loop visiting both is uniformly positive. Our results hold under general assumptions on the interaction potential, which may have bounded or unbounded support or introduce hard-core constraints.
