Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel...

We compute two- and three-point functions at criticality for the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model at the critical temperature on lattices of a linear size up to L=1600. As a check, also simulations of the spin-1/2 Ising model are performed. We find f_{σσε}=1.051(1) and f_{εεε}=1.533(5) for operator product expansion coefficients. These results are consistent with but less precise than those recently obtained by using the bootstrap method. An important ingredient in our simulations is a variance reduced estimator of N-point functions. Finite size corrections vanish with L^{-Δ_{ε}}, where L is the linear size of the lattice and Δ_{ε} is the scaling dimension of the leading Z_{2}-even scalar ε.