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arXiv · 2110.12109

Critical Three-Dimensional Ising Model on Spheriods from the Conformal Bootstrap

Daniel Berkowitz·George Fleming
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Abstract

We construct a conformal map from $\mathbb{R}^3$ to a three-dimensional spheriod, which includes $\mathbb{S}^3$, a double-cover of the 3-ball, and $\mathbb{R} \times \mathbb{S}^2$ as limiting cases. Using the data of the critical three-dimensional Ising model on $\mathbb{R}^3$ that was computed using the conformal bootstrap method, we numerically estimate the fourth-order Binder cumulant of the critical three-dimensional $\phi^4$ theory on $\mathbb{S}^3$. We expect this estimate will enable an interesting comparison between the conformal bootstrap and future calculations of critical $\phi^4$ theory on $\mathbb{S}^3$ using the Quantum Finite Element (QFE) method.

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Daniel Berkowitz, George Fleming. 2021-10-23. Critical Three-Dimensional Ising Model on Spheriods from the Conformal Bootstrap. https://arxiv.org/abs/2110.12109

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