论文标题
$ p $ - adic运营商及其$ p $ adic gibbs措施的定期点
Periodic points of a $p$-adic operator and their $p$-adic Gibbs measures
论文作者
论文摘要
在本文中，我们针对$ p $ - adc的硬核（HC）模型调查了广义吉布斯度量（GGM），并在订单$ k \ geq 2 $的卡利树上具有可数的旋转值。该模型由$ p $ -adic参数$λ_i$，$ i \ in \ mathbb n $定义。我们分析了$ p $ - 辅助功能方程，该方程提供了有限维gibbs分布的一致性条件。功能方程式的每个解决方案均通过$ p $ -ADIC版本的Kolmogorov定理定义了GGM。我们将$ p $ - adadic gibbs分布定义为有限维gibbs分布的一致家族的限制，并表明，对于我们在cayley树上的$ p $ - 亚种HC模型，这种Gibbs分布不存在。在某些条件下，参数$ p $，$ k $和$λ_i$，我们找到了$ p $ - ad的HC模型的翻译不动和两期ggm的数量。
In this paper we investigate generalized Gibbs measure (GGM) for $p$-adic Hard-Core(HC) model with a countable set of spin values on a Cayley tree of order $k\geq 2$. This model is defined by $p$-adic parameters $λ_i$, $i\in \mathbb N$. We analyze $p$-adic functional equation which provides the consistency condition for the finite-dimensional generalized Gibbs distributions. Each solutions of the functional equation defines a GGM by $p$-adic version of Kolmogorov's theorem. We define $p$-adic Gibbs distributions as limit of the consistent family of finite-dimensional generalized Gibbs distributions and show that, for our $p$-adic HC model on a Cayley tree, such a Gibbs distribution does not exist. Under some conditions on parameters $p$, $k$ and $λ_i$ we find the number of translation-invariant and two-periodic GGMs for the $p$-adic HC model on the Cayley tree of order two.
