  In this work we classify the singularities obtained from the Gibbs potential
of a lattice gas model with three components, two order parameters and five
control parameters applying the general theorems provided by Catastrophe
Theory. In particular, we clearly establish the existence of Landau potentials
in two variables or, in other words, corank 2 canonical forms that are
associated to the hyperbolic umbilic, D_{+4}, its dual the elliptic umbilic,
D_{-4}, and the parabolic umbilic, D_5, catastrophes. The transversality of the
potential with two order parameters is explicitely shown for each case. Thus we
complete the Catastrophe Theory analysis of the three-component lattice model,
initiated in a previous paper.
