Discretely holomorphic parafermions in lattice ZN models
Discretely holomorphic parafermions in lattice ZN models
复制标题
晶格 ZN 模型中的离散全纯拟费米子
DOI：
10.1088/1751-8113/40/49/006
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
J. Cardy
中科院分区：
文献类型：
--
作者：
M. Rajabpour;J. Cardy
我们构造了正则各向同性平面格上最近邻ZN模型中的格仿费米子--有序和无序算子的局部乘积，并证明了它们是离散全纯的，即它们恰好在临界Fateev-Zamolodchikov（FZ）可积点处满足离散Cauchy-Riemann方程.我们将我们的分析推广到各向异性相互作用的模型，表明，只要晶格是正确地嵌入在平面上，这种离散的全纯parafermions存在的特定值的耦合，我们确定为各向异性FZ点。这些结果扩展到更一般的非均匀晶格模型，只要覆盖晶格承认在平面上的菱形嵌入。
We construct lattice parafermions—local products of order and disorder operators—in nearest-neighbor ZN models on regular isotropic planar lattices and show that they are discretely holomorphic, that is they satisfy discrete Cauchy–Riemann equations, precisely at the critical Fateev–Zamolodchikov (FZ) integrable points. We generalize our analysis to models with anisotropic interactions, showing that, as long as the lattice is correctly embedded in the plane, such discretely holomorphic parafermions exist for particular values of the couplings which we identify as the anisotropic FZ points. These results extend to more general inhomogeneous lattice models as long as the covering lattice admits a rhombic embedding in the plane.