Scaling limit of the Ising model in a field

The dilute A(3) model is a solvable interaction round a face model with three local states and adjacency conditions encoded by the Dynkin diagram of the Lie algebra A(3). It can be regarded as a solvable spin-1 Ising model at the critical temperature in a magnetic field. One therefore expects the scaling limit to be governed by Zamolodchikov's integrable perturbation of the c = 1/2 conformal field theory. Indeed, a recent thermodynamic Bethe ansatz approach succeeded in unveiling the corresponding E-8 structure under certain assumptions on the nature of the Bethe ansatz solutions. In order to check these conjectures, we perform a detailed numerical investigation of the solutions of the Bethe ansatz equations for the critical and off-critical models. Scaling functions for the ground-state corrections and for the lowest spectral gaps are obtained, which give very precise numerical results for the lowest mass ratios in the massive scaling limit. While these agree perfectly with the E-8 mass ratios, we observe one state that seems to violate the assumptions underlying the thermodynamic Bethe ansatz calculation. We also analyze the critical spectrum of the dilute A(3) model, which exhibits excitations with a finite gap on top of the massless spectrum of the Ising conformal field theory.