Ising model on the affine plane

We demonstrate that the Ising model on a general triangular graph with three distinct couplings ${K}_{1}$, ${K}_{2}$, and ${K}_{3}$ corresponds to an affine transformed conformal field theory (CFT). Full invariance of $c=1/2$ minimal CFT is restored by introducing metric lattice through map $\mathrm{sinh}(2{K}_{i})={\ensuremath{\ell}}_{i}^{*}/{\ensuremath{\ell}}_{i}$ which relates critical ratio dual hexagonal edge lengths. Applied 2D toroidal lattice, this provides exact formulation in continuum limit as function modular parameter. This example can be viewed quantum generalization finite element method applied strong coupling at Wilson-Fisher IR fixed point suggests new approach curved manifolds based synthesis simplicial geometry projective tangent planes.