Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition
Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition
复制标题
DOI：
10.1103/physrevresearch.5.013086
复制
发表时间：
2022-02
影响因子：
4.2
通讯作者：
Zhiyuan Wang;K. Hazzard
中科院分区：
文献类型：
--
作者：
Zhiyuan Wang;K. Hazzard
我们研究了一个三维经典伊辛模型，当某些耦合常数取一定的虚值时，该模型是完全可解的。该解决方案结合和推广的Onsager-Kaufman解决方案的二维伊辛模型和Kitaev的蜂窝模型的解决方案，导致一个三参数相图与两个不同的阶段之间的第三级相变。有趣的是，这个模型的相位是由拓扑特征区分的：某个回路可观测量族的期望值仅取决于回路的拓扑（回路是否可收缩），并且在两个相位不同的有理值处量化。我们发现，一个相关的精确可解的三维经典统计模型与真实的耦合常数也显示了这些阶段之一的拓扑特征。此外，即使在具有复杂参数的模型中，配分函数也具有一些物理相关性，因为它可以被解释为量子动力学过程的跃迁幅度，并且可以揭示动态量子相变。
We study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution of the 2D Ising model and the solution of Kitaev's honeycomb model, leading to a three-parameter phase diagram with a third order phase transition between two distinct phases. Interestingly, the phases of this model are distinguished by topological features: the expectation value of a certain family of loop observables depend only on the topology of the loop (whether the loop is contractible), and are quantized at rational values that differ in the two phases. We show that a related exactly solvable 3D classical statistical model with real coupling constants also shows the topological features of one of these phases. Furthermore, even in the model with complex parameters, the partition function has some physical relevance, as it can be interpreted as the transition amplitude of a quantum dynamical process and may shed light on dynamical quantum phase transitions.