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The Ising Model on mathbb S²
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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.
Forward citations
Cited by 2 Pith papers
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Qubit discretizations of d=3 conformal field theories
A protocol extracts scaling dimensions of d=3 CFTs from the spectrum of qubit Hamiltonians on polyhedral lattices, achieving few-percent accuracy on the 3D Ising model with 20 qubits.
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