论文标题
伊辛模型的颜色表示
Color representations of Ising models
论文作者
论文摘要
在\ cite {st2017}中，作者介绍了所谓的\ emph {常规鸿沟和颜色模型}。这种模型的最著名示例之一是具有外部字段$ h = 0 $的ISING模型，该模型具有随机群集模型给出的颜色表示。在本文中，我们提供了必要的条件，使这种颜色表示是唯一的。我们还表明，如果一个人在完整的图表上考虑了Ising模型，那么对于许多$ H> 0 $，则没有颜色表示。这特别表明，对随机群集模型的任何概括都提供了具有外部字段的ISING模型的颜色表示形式，通常不能是广义的鸿沟和颜色模型。此外，我们表明，最多可以有限的许多$β> 0 $，可以将随机群集模型连续扩展到颜色表示形式，以$ h \ not = 0 $。
In \cite{st2017}, the authors introduced the so-called \emph{general divide and color models}. One of the most well-known examples of such a model is the Ising model with external field $h = 0$, which has a color representation given by the random cluster model. In this paper, we give necessary and sufficient conditions for this color representation to be unique. We also show that if one considers the Ising model on a complete graph, then for many $h > 0$, there is no color representation. This shows in particular that any generalization of the random cluster model which provides color representations of Ising models with external fields cannot, in general, be a generalized divide and color models. Furthermore, we show that there can be at most finitely many $β> 0$ at which the random cluster model can be continuously extended to a color representation for $h \not = 0$.
