Critical amplitudes and mass spectrum of the 2d Ising model in a magnetic field

We compute the spectrum and several critical amplitudes of the two-dimensio nal Ising model in a magnetic field with the transfer matrix method. The th ree lightest masses End their overlaps with the spin and the energy operato rs are computed on lattices of a width up to L-1 = 21. In extracting the co ntinuum results we also take into account the corrections to scaling due to irrelevant operators. In contrast with previous Monte Carlo simulations ou r final results are in perfect agreement with the predictions of S-matrix a nd conformal field theory. We also obtain the amplitudes of some of the sub leading corrections, for which no S-matrix prediction has yet been obtained . (C) 2000 Elsevier Science B.V. All rights reserved.