  We study the spin-spin, spin-energy and energy-energy correlators in the 2d
Ising model perturbed by a magnetic field. We compare the results of a set of
high precision Montecarlo simulations with the predictions of two different
approximations: the Form Factor approach, based on the exact S-matrix
description of the model, and a short distance perturbative expansion around
the conformal point. Both methods give very good results, the first one
performs better for distances larger than the correlation length, while the
second one is more precise for distances smaller than the correlation length.
In order to improve this agreement we extend the perturbative analysis to the
second order in the derivatives of the OPE constants.
