  The free energy and local height probabilities of the dilute A models with
broken $\Integer_2$ symmetry are calculated analytically using inversion and
corner transfer matrix methods. These models possess four critical branches.
The first two branches provide new realisations of the unitary minimal series
and the other two branches give a direct product of this series with an Ising
model. We identify the integrable perturbations which move the dilute A models
away from the critical limit. Generalised order parameters are defined and
their critical exponents extracted. The associated conformal weights are found
to occur on the diagonal of the relevant Kac table. In an appropriate regime
the dilute A$_3$ model lies in the universality class of the Ising model in a
magnetic field. In this case we obtain the magnetic exponent $\delta=15$
directly, without the use of scaling relations.
