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

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.