MAGNETIZATION OF MESOSCOPIC DISORDERED NETWORKS

We study the magnetic response of mesoscopic metallic isolated network s. We calculate the average and typical magnetizations in the diffusiv e regime for non-interacting electrons or in the first-order Hartree-F ock approximation. These quantities are related to the return probabil ity for a diffusive particle on the corresponding network. By solving the diffusion equation on various types of networks, Including a ring with arms, an infinite square network or a chain of connected rings, w e deduce the corresponding magnetizations. In the case of an infinite network, the Hartree-Fock average magnetization stays finite in the th ermodynamic limit. We discuss the relevance of our results to the expe rimental situation. Quite generally, when rings are connected, the ave rage magnetization is only weakly reduced by a numerical factor.