Phase transitions in the frustration network

The distribution of the frustrated plaquettes is calculated as a function of disorder for two and three dimensional random Ising- andXY-models. It is shown that in all cases the frustrated plaquettes are highly correlated and that at a critical value of disorder a phase transition occurs in the frustration network which can be viewed as a dissociation of plaquettes. The critical disorder is calculated using duality transformations. We show that in the two and three dimensional random Ising systems two types of nonmagnetic phases exist which differ qualitatively by their distribution of frustrated plaquettes and consequently by their domain wall structure.