Numerical determination of the operator-product-expansion coefficients in the 3D Ising model from off-critical correlators

We propose a general method for the numerical evaluation of OPE 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 <σ(r)σ(0)>, <σ(r)ϵ(0)> and <ϵ(r)ϵ(0)> correlators from which we extract the values of Cσσϵ=1.07(3) and Cϵϵϵ=1.45(30). Our estimate for Cσσϵ agrees with those recently obtained using conformal bootstrap methods, while Cϵϵϵ, as far as we know, is new and could be used to further constrain conformal bootstrap analyses of the 3d Ising universality class.