Bootstrapping the 3d Ising model at finite temperature

Abstract

We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions $⟨\sigma \sigma ⟩$ and $⟨\epsilon \epsilon ⟩$. As a result, we estimate the one-point functions of the lowest-dimension ${\mathbb{Z}}_2$-even scalar $\epsilon$ and the stress-energy tensor $T_{\mu \nu }$. Our result for $⟨\sigma \sigma ⟩$ at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.

arXiv comment34 pages, 13 figures, 1 table

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• Dispersive CFT Sum Rules
• The critical O(N) CFT: Methods and conformal data
• Gravitational orbits, double-twist mirage, and many-body scars
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Universal Asymptotics for High Energy CFT Data
• Distributions in CFT II. Minkowski Space
• Holographic Correlators at Finite Temperature
• Thermalization in Large-N CFTs
• Mixed Scalar-Current bootstrap in three dimensions
• Black hole bulk-cone singularities
• Conformal Bootstrap near the edge
• Thermal CFTs in momentum space
• Ising model close to $d=2$
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• The thermal bootstrap for the critical O(N) model
• Conformal line defects at finite temperature
• Finite Temperature at Finite Places
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations