Bootstrapping the 3d Ising Stress Tensor

Abstract

We compute observables of the critical 3d Ising model to high precision by applying the numerical conformal bootstrap to mixed correlators of the leading scalar operators $\sigma$ and $\epsilon$, and the stress tensor $T_{\mu \nu }$. We obtain new precise determinations of scaling dimensions $({\Delta }_{\sigma },{\Delta }_{\epsilon })=(0.518148806(24),1.41262528(29))$ as well as OPE coefficients involving $\sigma$, $\epsilon$, and $T_{\mu \nu }$. We also describe several improvements made along the way to algorithms and software tools for the numerical bootstrap.

52 pages, 10 figures, 9 tables; v2: small updates to match JHEP version

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• The tricritical Ising CFT and conformal bootstrap
• The thermal bootstrap for the critical O(N) model
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Three-dimensional real space renormalization group with well-controlled approximations
• Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids
• Lee-Yang-zero ratio method in three-dimensional Ising model
• Sparsity in the numerical six-point bootstrap
• A Fuzzy Sphere Journey in Critical Phenomena
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Detecting the Largest Correlations using the Correlation Density Matrix: a Quantum Monte Carlo Approach
• Supercritical-subcritical correspondence, asymmetric effects and antisymmetric corrections near a critical point
• Moments and saddles of heavy CFT correlators
• Ising Supercriticality and Universal Magnetocalorics in Spiral Antiferromagnet Nd${}_3$BWO${}_9$
• 100 Glorious Years of the Ising Model
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models
• Conformal Bootstrap with Duality-Inspired Fusion Rule
• Relationship between Heider links and Ising spins
• On the Wilson-Fisher fixed point in the limit of integer spacetime dimensions