耦合到伊辛模型的二维相变
Phase transitions in 2d orders coupled to the Ising model
摘要：
$2$ d阶是因果集的一个子类，它特别适合于计算机模拟。过去的工作已经表明，$2$ d级具有在随机相和结晶相之间的第一级相变。当将$2$ d阶耦合到伊辛模型时，该相变与伊辛模型的相变一致。在负$β$处，耦合系统还出现了一个新的相位，在此相位处，伊辛模型引起了几何相变。在这篇文章中，我们研究的相变的耦合系统，以确定其顺序，以及如何缩放时，系统的大小是改变的。我们发现正$β$的跃迁似乎是混合级的，而负$β$的两个跃迁对于伊辛模型和几何分别是连续级和一级的.另一方面，观测量与系统尺寸的比例相当简单，并且在适用的情况下，与纯$2$ d阶的结果一致。我们发现，这些转变的位置有分数标度的系统大小。
英文摘要：
The $2$d orders are a sub class of causal sets, which is especially amenable to computer simulations. Past work has shown that the $2$d orders have a first order phase transition between a random and a crystalline phase. When coupling the $2$d orders to the Ising model, this phase transition coincides with the transition of the Ising model. The coupled system also shows a new phase, at negative $β$, where the Ising model induces the geometric transition. In this article we examine the phase transitions of the coupled system, to determine their order, as well as how they scale when the system size is changed. We find that the transition at positive $β$ seems to be of mixed order, while the two transitions at negative $β$ appear continous/ first order for the Ising model/ the geometry respectively. The scaling of the observables with the system size on the other hand is fairly simple, and does, where applicable, agree with that found for the pure $2$d orders. We find that the location of these transitions has fractional scaling in the system size.
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