论文标题
部分可观测时空混沌系统的无模型预测
Topological correlations in three dimensional classical Ising models: an exact solution with a continuous phase transition
论文作者
论文摘要
我们研究了三维（3D）经典模型，当某些耦合常数采用某些假想值时，该模型是可以解决的。该解决方案结合了2D ISING模型的Onsager-Kaufman解决方案和Kitaev蜂窝模型的解决方案，从而导致三参数相图在两个不同的相之间具有三阶相变。有趣的是，该模型的阶段是由拓扑特征区别的：特定环路可观察的家族的期望值仅取决于环路的拓扑（是否可违约），并以在两个阶段不同的合理值进行量化。我们表明，具有实际耦合常数的准确可解决的3D经典统计模型还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，分区函数也具有一定的物理相关性，因为它可以解释为量子动态过程的过渡幅度，并且可能会阐明动态量子相变。
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.
