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

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(sigma sigma epsilon) = = 1.051( 1) and f(epsilon epsilon epsilon) = 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-Delta epsilon, where L is the linear size of the lattice and Delta(epsilon) is the scaling dimension of the leading Z(2)-even scalar epsilon.