Cluster formulation of spin glasses and the frustrated percolation model: statics and dynamics

We study the properties of the q-state frustrated bond percolation model by a Monte Carlo 'bond flip' dynamics, using an algorithm originally devised by Sweeny and suitably modified to treat the presence of frustration. For q = 2 the model gives the cluster formulation of the Edwards-Anderson spin glass. We analyse the percolation transition of the model, and find that it falls in the universality class of the q/2-state ferromagnetic Potts model. We then investigate the bond flip dynamics of the model, and find that, while for temperatures higher than the percolation transition, T-p, the relaxation functions are fitted by a single exponential; for T < T-p they show a two-step decay, reminiscent of the relaxation of glass-forming liquids. The long time decay (alpha-relaxation) is well fitted for T < T-p by a stretched exponential function, showing that in this model the relevant mechanism for the appearance of stretched exponentials is the percolation transition. At very low temperatures the relaxation functions develop a long plateau, as observed in glass-forming liquids.