  $2$-form abelian and non-abelian gauge fields on $d$-dimensional hypercubic
lattices have been discussed in the past by various authors and most recently
by Lipstein and Reid-Edwards. In this note we recall that the Hamiltonian of a
$\mathbb{Z}_2$ variant of such theories is one of the family of generalized
Ising models originally considered by Wegner. For such "$\mathbb{Z}_2$ lattice
gerbe theories" general arguments can be used to show that a phase transition
for Wilson surfaces will occur for $d>3$ between volume and area scaling
behaviour. In $3d$ the model is equivalent under duality to an infinite
coupling model and no transition is seen, whereas in $4d$ the model is dual to
the $4d$ Ising model and displays a continuous transition. In $5d$ the
$\mathbb{Z}_2$ lattice gerbe theory is self-dual in the presence of an external
field and in $6d$ it is self-dual in zero external field.
