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

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 ${\varphi }^4$ theory on ${\mathbb{S}}^3$. We expect this estimate will enable an interesting comparison between the conformal bootstrap and future calculations of critical ${\varphi }^4$ theory on ${\mathbb{S}}^3$ using the Quantum Finite Element (QFE) method.

Comments: 11 pages, 3 figures, Submitted to Physical Review D