论文标题
相结合与Ising模型的2D订单中的相变
Phase transitions in 2d orders coupled to the Ising model
论文作者
论文摘要
$ 2 $ d的订单是因果集的子类别，特别适合计算机模拟。过去的工作表明，$ 2 $ d的订单在随机和结晶相之间具有一阶相变。当将$ 2 $ D的订单耦合到Ising模型时，此相转换与Ising模型的过渡一致。耦合系统还显示了一个新的阶段，即负$β$，其中Ising模型诱导了几何跃迁。在本文中，我们检查了耦合系统的相变，以确定它们的顺序以及在更改系统大小时如何扩展。我们发现，正$β$下的过渡似乎是混合的顺序，而在$β$上的两个转换分别为ISING模型/几何形状看起来连续/一阶。另一方面，可观察到系统尺寸的可观测值的缩放相当简单，并且在适用的情况下确实与纯$ 2 $ d订单相一致。我们发现这些过渡的位置具有系统尺寸的分数缩放。
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.
