We propose a general method for the numerical evaluation of operator product expansion coefficients in three dimensional conformal field theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point. We test our proposal in the three dimensional Ising model, looking at the magnetic perturbation of the $⟨\sigma (\mathbf{r})\sigma (0)⟩$, $⟨\sigma (\mathbf{r})\epsilon (0)⟩$ and $⟨\epsilon (\mathbf{r})\epsilon (0)⟩$ correlators from which we extract the values of $C_{\sigma \epsilon }^{\sigma }=1.07(3)$ and $C_{\epsilon \epsilon }^{\epsilon }=1.45(30)$. Our estimate for $C_{\sigma \epsilon }^{\sigma }$ agrees with those recently obtained using conformal bootstrap methods, while $C_{\epsilon \epsilon }^{\epsilon }$, as far as we know, is new and could be used to further constrain conformal bootstrap analyses of the 3d Ising universality class.

• Received 28 January 2015

DOI:https://doi.org/10.1103/PhysRevD.91.061901