  The dilute A_3 model is a solvable IRF (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 version of an 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 to unveil 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
model. 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 which 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 massive
excitations on top of the massless states of the Ising conformal field theory.
