SCALING LIMIT OF THE ISING-MODEL IN A FIELD

The dilute A(3) model is a solvable interaction round a face model wit h three local states and adjacency conditions encoded by the Dynkin di agram 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 ther efore expects the scaling limit to be governed by Zamolodchikov's inte grable perturbation of the c = 1/2 conformal field theory. Indeed, a r ecent thermodynamic Bethe ansatz approach succeeded in unveiling the c orresponding E-8 structure under certain assumptions on the nature of the Bethe ansatz solutions. In order to check these conjectures, we pe rform a detailed numerical investigation of the solutions of the Bethe ansatz equations for the critical and off-critical models. Scaling fu nctions for the ground-state corrections and for the lowest spectral g aps are obtained, which give very precise numerical results for the lo west mass ratios in the massive scaling limit. While these agree perfe ctly with the E-8 mass ratios, we observe one state that seems to viol ate the assumptions underlying the thermodynamic Bethe ansatz calculat ion. We also analyze the critical spectrum of the dilute A(3) model, w hich exhibits excitations with a finite gap on top of the massless spe ctrum of the Ising conformal field theory.