Inhomogeneous transitions in extremely disordered media

A high degree of disorder in the coupling energies of a ferromagnetic glass favors the formation of clusters with the highest possible coupling energies. This defines a percolation transition which proceeds simultaneously with the thermal one. The former provides a constraining fractal dimensionality $D$ for the latter; as a result, the critical exponent for the correlation length is larger than in the usual homogeneous case. Predictions of the $\frac{1}{n}$ expansion with dimensionality $D$ are in good agreement with experimental results on granular superconductors.