A model of loops in 2-D

Abstract

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.