On gonihedric loops and quantum gravity

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 cmatter = 0 for all values of the parameters of the model. In this way it is possible to understand the absence of a continuous transition