It is shown that the field theory describing the scaling limit of T = T c Ising model with nonzero magnetic field possesses a number of nontrivial local integrals of motion. The exact mass spectrum and S-matrix of this field theory is conjectured.
We compute the spectrum and several critical amplitudes of the two dimensional Ising model in a magnetic field with the transfer matrix method. The three lightest masses and their overlaps with the spin and the energy operators are computed on lattices of a width up to L=21. In extracting the continuum results we also take into account the corrections to scaling due to irrelevant operators. In contrast with previous Monte Carlo simulations our final results are in perfect agreement with the predictions of S-matrix and conformal field theory. We also obtain the amplitudes of some of the subleading corrections, for which no S-matrix prediction has yet been obtained.