The dilute A₄ model, the E₇ mass spectrum and the tricritical Ising model

The exact perturbation approach is used to derive the (seven) elementary correlation lengths and related mass gaps of the two-dimensional dilute A$_4$ lattice model in regime 2- from the Bethe ansatz solution. This model provides a realisation of the integrable $\phi(1,2)$ perturbation of the c=7/10 conformal field theory, which is known to describe the off-critical thermal behaviour of the tricritical Ising model. The E$_7$ masses predicted from purely elastic scattering theory follow in the approach to criticality. Universal amplitudes for the tricritical Ising model are calculated.