  We investigate a 3d Ising action which corresponds to a a class of models
defined by Savvidy and Wegner, originally intended as discrete versions of
string theories on cubic lattices. These models have vanishing bare surface
tension and the couplings are tuned in such a way that the action depends only
on the angles of the discrete surface, i.e. on the way the surface is embedded
in ${\bf Z}^3$. Hence the name gonihedric by which they are known. We show that
the model displays a rather clear first order phase transition in the limit
where self-avoidance is neglected and the action becomes a plaquette one. This
transition persists for small values of the self avoidance coupling, but it
turns to second order when this latter parameter is further increased. These
results exclude the use of this type of action as models of gonihedric random
surfaces, at least in the limit where self avoidance is neglected.
