  A state sum construction on closed manifolds \'{a} la Kuperberg can be used
to construct the partition functions of $3D$ lattice gauge theories based on
involutory Hopf algebras, $\mathcal{A}$, of which the group algebras,
$\mathbb{C}G$, are a particular case. Transfer matrices can be obtained by
carrying out this construction on a manifold with boundary. Various
Hamiltonians of physical interest can be obtained from these transfer matrices
by playing around with the parameters the transfer matrix is a function of. The
$2D$ quantum double Hamiltonians of Kitaev can be obtained from such transfer
matrices for specific values of these parameters. A initial study of such
models has been carried out in \cite{p1}. In this paper we study other regions
of this parameter space to obtain some new and known models. The new model
comprise of Hamiltonians which "partially" confine the excitations of the
quantum double Hamiltonians which are usually deconfined. The state sum
construction allows for parameters depending on the position in obtaining the
transfer matrices and thus it is natural to expect disordered Hamiltonians from
them. Thus one set of known models consist of the disordered quantum double
Hamiltonians. Finally we obtain quantum double Hamiltonians perturbed by
magnetic fields which have been considered earlier in the literature to study
the stability of topological order to perturbations.
