The Ising Model on ${\mathbb{S}}^2$

Abstract

We define a 2-dimensional Ising model on a triangulated sphere, ${\mathbb{S}}^2$, designed to approach the exact conformal field theory (CFT) in the continuum limit. Surprisingly, the derivation leads to a set of geometric constraints that the lattice field theory must satisfy. Monte Carlo simulations are in agreement with the exact Ising CFT on ${\mathbb{S}}^2$. We discuss the inherent benefits of using non-uniform simplicial lattices and how these methods may be generalized for use with other quantum theories on curved manifolds.

23 pages, 14 figures