The Ising Model on $\mathbb S^2$

Richard C. Brower; Evan K. Owen

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arXiv · 2407.00459

The Ising Model on $\mathbb S^2$

Richard C. Brower·Evan K. Owen

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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.

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Richard C. Brower, Evan K. Owen. 2024-06-29. The Ising Model on $\mathbb S^2$. https://arxiv.org/abs/2407.00459

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