论文标题
在情况棒的三态硬核模型的周期性吉布斯量度
Periodic Gibbs measures for three-state hard-core models in the case Wand
论文作者
论文摘要
我们考虑使用活动参数$λ> 0 $上的肥沃的三州硬核（HC）模型。众所周知，存在四种类型的模型：扳手，魔杖，铰链和管道。这些模型作为最接近邻居排除的损失网络的简单示例。在订单$ k \ geq2 $的Cayley树上的情况下，发现了确切的临界值$λ> 0 $，对于两个周期性的Gibbs测量并非唯一。此外，我们研究了二级订单的Cayley树上现有的两周期吉布斯测量的极端。
We consider fertile three-state Hard-Core (HC) models with the activity parameter $λ>0$ on a Cayley tree. It is known that there exist four types of such models: wrench, wand, hinge, and pipe. These models arise as simple examples of loss networks with nearest-neighbor exclusion. In the case wand on a Cayley tree of order $k\geq2$, exact critical values $λ>0$ are found for which two-periodic Gibbs measures are not unique. Moreover, we study the extremality of the existing two-periodic Gibbs measures on a Cayley tree of order two.
