  The gonihedric spin model was first introduced as the action for a
discretized tensionless string in a discretized embeding space. Afterwards was
found that there are interesting features on the dynamical behavior of this
model in 3 dimensions (as it was first formulated) that make us think on glassy
spin model without inherent disorder. Extensive simulations have been carried
out in the 3 dimensional model. In the following I will report on a work
composed of two different but related parts. The first part is a numerical
study through Monte Carlo simulations of the dynamical properties of the 2
dimensional version of the model (i.e. the loop model), which is much simpler
due to the fact that it has trivial thermodynamical properties. The second part
consists on an analytical approach of this 2 dimensional loop model coupled to
gravity. We solve partially the associated two-matrix model via a reduction to
an equivalent one matrix model and saddle point methods with the last
one-matrix model.
