Conformal perturbation of off-critical correlators in the 3D Ising universality class

Abstract

Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly precise estimates for off-critical correlators using conformal perturbation. We discuss in particular the $<\sigma (r)\sigma (0)>$, $<\epsilon (r)\epsilon (0)>$ and $<\sigma (r)\epsilon (0)>$ two point functions in the high and low temperature regimes of the 3D Ising model and evaluate the leading and next to leading terms in the $s=t{r}^{{\Delta }_t}$ expansion, where $t$ is the reduced temperature. Our results for $<\sigma (r)\sigma (0)>$ agree both with Monte Carlo simulations and with a set of experimental estimates of the critical scattering function.

4 pages, 2 figures, Expanded the discussion of Conformal Perturbation Theory

References in corpus (6)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• More constraining conformal bootstrap
• Bootstrapping the O(N) Archipelago
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• OPE Coefficients of the 3D Ising model with a trapping potential

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• Conformal perturbation theory
• Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions
• Confining strings in three-dimensional gauge theories beyond the Nambu--Gotō approximation
• Conformal perturbation theory confronts lattice results in the vicinity of a critical point
• Energy trapped Ising model