# Bootstrapping the 3d Ising model at finite temperature

## Author:

Iliesiu, L
Kologlu, M
Simmons-Duffin, D

9 December 2019

## Journal:

JOURNAL OF HIGH ENERGY PHYSICS

## Last Updated:

2021-10-19T13:23:46.86+01:00

12

2019

## DOI:

10.1007/JHEP12(2019)072

## abstract:

© 2019, The Author(s). 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 〈σσ〉 and 〈ϵϵ〉. As a result, we estimate the one-point functions of the lowest-dimension ℤ2-even scalar ϵ and the stress energy tensor Tμν. Our result for 〈σσ〉 at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.

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