论文标题
具有可计数旋转值集的HC模型：无数的吉布斯度量
A HC model with countable set of spin values: uncountable set of Gibbs measures
论文作者
论文摘要
我们考虑使用Cayley树上旋转值的可数集$ \ Mathbb {z} $的硬核（HC）模型。该模型由可数的参数集$λ_{i}> 0，i \ in \ Mathbb {z} \ setMinus \ {0 \} $定义。对于参数的所有可能值，我们给出了由函数生成的动力系统的限制点，该函数描述了有限维度测量的一致性条件。另外，我们证明，给定模型的每个定期吉布斯度量都是翻译不变的，或者是周期二。此外，我们为此HC模型构建了无数的Gibbs度量。
We consider a hard core (HC) model with a countable set $\mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $λ_{i}>0, i \in \mathbb{Z}\setminus\{0\}$. For all possible values of parameters, we give limit points of the dynamical system generated by a function which describes the consistency condition for finite-dimensional measures. Also, we prove that every periodic Gibbs measure for the given model is either translation-invariant or periodic with period two. Moreover, we construct uncountable set of Gibbs measures for this HC model.
