论文标题
仿射平面上的模型
Ising Model on the Affine Plane
论文作者
论文摘要
我们证明，具有3个不同耦合的一般三角形图上的Ising模型$ k_1，k_2，k_3 $对应于仿射转化的保形场理论（CFT）。 $ c = 1/2 $的完全整形不变性通过在晶格上通过地图$ \ sinh（2k_i）= \ ell^*_ i/ \ ell_i $引入指标，从而恢复了最小的CFT，这将关键耦合与双重六边形和三角形边缘长度相关。应用于2D环形晶状体，这在连续限制中为ISING CFT提供了一个精确的晶格公式，作为模块化参数的函数。可以将此示例视为在Wilson-Fisher IR固定点上应用于强耦合CFT的有限元方法（FEM）的量子概括，并提出了一种基于简单几何形状和切线平面上的简单几何形状和投射几何形状的融合的曲线歧管上的共形场理论的新方法。
We demonstrate that the Ising model on a general triangular graph with 3 distinct couplings $K_1,K_2,K_3$ corresponds to an affine transformed conformal field theory (CFT). Full conformal invariance of the $c= 1/2$ minimal CFT is restored by introducing a metric on the lattice through the map $\sinh(2K_i) = \ell^*_i/ \ell_i$ which relates critical couplings to the ratio of the dual hexagonal and triangular edge lengths. Applied to a 2d toroidal lattice, this provides an exact lattice formulation in the continuum limit to the Ising CFT as a function of the modular parameter. This example can be viewed as a quantum generalization of the finite element method (FEM) applied to the strong coupling CFT at a Wilson-Fisher IR fixed point and suggests a new approach to conformal field theory on curved manifolds based on a synthesis of simplicial geometry and projective geometry on the tangent planes.
