Cluster formulation for frustrated spin models

A q-state frustrated Potts model is introduced which generalizes the Kasteleyn-Fortuin formalism to frustrated systems. For q = 2 the Ising spin is recovered. For q = 1 it gives the frustrated percolation model, which combines frustration and connectivity features and might be relevant to systems like gels of glasses. The solution on a decorated lattice shows that a line of critical temperatures Tp(q) appears when frustration is introduced. Tp(q) is the percolation temperature where the clusters used in the Swendsen and Wang dynamics diverge. The critical behaviour at Tp(q) is found to be the same as the ferromagnetic q2 state Potts model, implying the universality class of the ferromagnetic 12 state Potts model for frustrated percolation.