Critical ThreeDimensional Ising Model on Spheriods from the Conformal Bootstrap
Abstract
We construct a conformal map from $\mathbb{R}^3$ to a threedimensional spheriod, which includes $\mathbb{S}^3$, a doublecover of the 3ball, and $\mathbb{R} \times \mathbb{S}^2$ as limiting cases. Using the data of the critical threedimensional Ising model on $\mathbb{R}^3$ that was computed using the conformal bootstrap method, we numerically estimate the fourthorder Binder cumulant of the critical threedimensional $\phi^4$ 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.12109
 Bibcode:
 2021arXiv211012109B
 Keywords:

 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 11 pages, 3 figures, Submitted to Physical Review D