# The Ising Model on $S^2$ - The Affine Conjecture

### APA

Brower, R. (2024). The Ising Model on $S^2$ - The Affine Conjecture. Perimeter Institute. https://pirsa.org/24040102

### MLA

Brower, Richard. The Ising Model on $S^2$ - The Affine Conjecture. Perimeter Institute, Apr. 19, 2024, https://pirsa.org/24040102

### BibTex

@misc{ pirsa_PIRSA:24040102, doi = {10.48660/24040102}, url = {https://pirsa.org/24040102}, author = {Brower, Richard}, keywords = {Condensed Matter}, language = {en}, title = {The Ising Model on $S^2$ - The Affine Conjecture}, publisher = {Perimeter Institute}, year = {2024}, month = {apr}, note = {PIRSA:24040102 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

A formulation of the 2-dimensional Ising model on a triangulated Riemann sphere is proposed that converges to the exact conformal field theory (CFT) in the continuum limit. The solution is based on reconciling Regge's simplicial geometry for the Einstein Hilbert action with an Affine map to quantum correlators on the tangent plane. Numerical tests of the 2d Ising sphere and radial quantized phi4 theory on $R x S^2$ are presented. Extending the method to more general fields theories on curved manifolds is discussed.

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