论文标题
关于平面Ashkin-Teller模型中的边界相关性
On boundary correlations in planar Ashkin-Teller models
论文作者
论文摘要
我们将Griffith，Hurst和Sherman的开关引理推广到Ashkin-Teller模型的随机电流表示。然后，我们将其与二维拓扑的属性一起使用，以得出平面模型中多点边界旋转相关性和批量订购相关性的线性关系。我们还表明，Pfaffians的产品满足了相同的线性关系。结果，在两个独立的ISING模型的非互动情况下，出现了清晰的图片，其中Pfaffians和其各自的两点函数的决定因素给出了多点相关函数。这给出了对经典的Pfaffian身份和最新的总阳性不平等的统一处理，用于平面ISING模型中边界自旋相关性。我们还为具有负四体耦合常数的一般Ashkin Teller模型得出了Simon和Gaussian的不平等。
We generalize the switching lemma of Griffiths, Hurst and Sherman to the random current representation of the Ashkin-Teller model. We then use it together with properties of two-dimensional topology to derive linear relations for multi-point boundary spin correlations and bulk order-disorder correlations in planar models. We also show that the same linear relations are satisfied by products of Pfaffians. As a result a clear picture arises in the noninteracting case of two independent Ising models where multi-point correlation functions are given by Pfaffians and determinants of their respective two-point functions. This gives a unified treatment of both the classical Pfaffian identities and recent total positivity inequalities for boundary spin correlations in the planar Ising model. We also derive the Simon and Gaussian inequality for general Ashkin-Teller models with negative four-body coupling constants.
