  We present an analysis of the gonihedric loop model, a reformulation of the
two dimensional gonihedric spin model, using two different techniques. First,
the usual regular lattice statistical physics problem is mapped onto a height
model and studied analytically. Second, the gravitational version of this loop
model is studied via matrix models techniques. Both methods lead to the
conclusion that the model has $c_{matter}=0$ for all values of the parameters
of the model. In this way it is possible to understand the absence of a
continuous transition.
