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.

arXiv comment11 pages, 3 figures, Submitted to Physical Review D

References in corpus (14)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Solving the 3D Ising Model with the Conformal Bootstrap
• Precision Islands in the Ising and $O(N)$ Models
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Massive Field-Theory Approach to Surface Critical Behavior in Three-Dimensional Systems
• Surface and bulk transitions in three-dimensional O(n) models
• The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
• Dimensional Reduction for Conformal Blocks
• Lattice Radial Quantization: 3D Ising
• Lattice Dirac Fermions on a Simplicial Riemannian Manifold
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• Lattice ${\varphi }^4$ Field Theory on Riemann Manifolds: Numerical Tests for the 2-d Ising CFT on ${\mathbb{S}}^2$
• OPE Coefficients of the 3D Ising model with a trapping potential
• Improved Lattice Radial Quantization