The inversion relation and the dilute A(3,4,6) eigenspectrum

On the basis of the result obtained by applying Baxter's exact perturbative approach to the dilute A(3) model to give the E-8 mass spectrum, thr dilut e A(L) inversion relation was used to predict the eigenspectra in the L=4 a nd L=6 cases (corresponding to E-7 and E-6 respectively). In calculating th e next-to-leading term in the correlation lengths, or equivalently masses, the inversion relation condition gives a surprisingly simple result in all three cases, and for all masses.