论文标题
立方体移动$ s $ embeddings和$α$ - 真实性
Cube moves for $s$-embeddings and $α$-realizations
论文作者
论文摘要
切尔卡克（Chelkak）将$ s $ embeddings引入了切线四边形的斜利，这些四边形提供了正确的设置，可以在任意平面图上使用任意耦合常数研究ISING模型。我们证明了$ s $ embeddings的本地转换的存在和唯一性，称为Cube Move，其中包括翻转三个四边形的方式，以至于所得的平铺也在$ s $ embeddings的类中。顺便说一句，我们为Ising Star-Triangle变换的耦合常数更改提供了一个新的，更简单的公式，该耦合常数以$ s $ embeddings的形式连接到Cube Move。我们更普遍地介绍了$α$ - 将$α$的式介绍为一部分飞机的倾斜度，以使每个四边形$ abcd $的侧面长度满足$ ab^α+cd^α+cd^α= ad^aD^aD^α+bc^α$的关系，并为$ harmonic networks = harmonic networks = poss of AdapeDing network a podaped and possevers（$ a） $ s $ - embeddings（$α= 1 $）。我们研究了这些$α$ - 安装的立方体移动的存在和唯一性能。
Chelkak introduced $s$-embeddings as tilings by tangential quads which provide the right setting to study the Ising model with arbitrary coupling constants on arbitrary planar graphs. We prove the existence and uniqueness of a local transformation for $s$-embeddings called the cube move, which consists in flipping three quadrilaterals in such a way that the resulting tiling is also in the class of $s$-embeddings. In passing, we give a new and simpler formula for the change in coupling constants for the Ising star-triangle transformation which is conjugated to the cube move for $s$-embeddings. We introduce more generally the class of $α$-embeddings as tilings of a portion of the plane by quadrilaterals such that the side lengths of each quadrilateral $ABCD$ satisfy the relation $AB^α+CD^α=AD^α+BC^α$, providing a common generalization for harmonic embeddings adapted to the study of resistor networks ($α=2$) and for $s$-embeddings ($α=1$). We investigate existence and uniqueness properties of the cube move for these $α$-embeddings.
