论文标题
离散旋转系统中的远程顺序
Long-range order in discrete spin systems
论文作者
论文摘要
我们在$ \ mathbb {z}^d $上建立了离散邻居旋转系统的远程顺序，当尺寸$ d $高于明确描述的阈值时，满足某个对称性假设的延长订单。结果表征了系统的所有周期性，最大压力的吉布斯状态。结果进一步适用于低维，但前提是晶格$ \ mathbb {z}^d $被$ \ m artbb {z}^{d_1} \ times \ times \ times \ times \ times \ times \ time \ time \ timbb {t}^{d_2 {d_2} $，用$ d_1 \ ge 2 $ d_1 \ ge 2 $ d_1+d_1+d_1+d_1+d_2 $ a，$甚至长度。详细讨论了针对特定系统的应用，并为其提供了新的结果，其中包括抗磁性POTTS模型，Lipschitz高度功能以及硬核，宽洛林 - 洛林森和海滩型号及其多类型扩展。我们还建立了詹森（Jenssen）和凯瓦什（Keevash）对高维极限的拓扑压力的公式。
We establish long-range order for discrete nearest-neighbor spin systems on $\mathbb{Z}^d$ satisfying a certain symmetry assumption, when the dimension $d$ is higher than an explicitly described threshold. The results characterize all periodic, maximal-pressure Gibbs states of the system. The results further apply in low dimensions provided that the lattice $\mathbb{Z}^d$ is replaced by $\mathbb{Z}^{d_1}\times\mathbb{T}^{d_2}$ with $d_1\ge 2$ and $d=d_1+d_2$ sufficiently high, where $\mathbb{T}$ is a cycle of even length. Applications to specific systems are discussed in detail and models for which new results are provided include the antiferromagnetic Potts model, Lipschitz height functions, and the hard-core, Widom--Rowlinson and beach models and their multi-type extensions. We also establish a formula conjectured by Jenssen and Keevash for the topological pressure in the high-dimensional limit.
