Thermodynamics and Transport in Mesoscopic Disordered Networks
  We describe the effects of phase coherence on transport and thermodynamic properties of a disordered conducting network. In analogy with weak-localization correction, we calculate the phase coherence contribution to the magnetic response of mesoscopic metallic isolated networks. It is related to the return probability 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, we deduce the magnetic response. As it is the case for transport properties --weak-localization corrections or universal conductance fluctuations-- the magnetic response can be written in term of a single function S called spectral function which is related to the spatial average of the return probability on the network. We have found that the magnetization of an ensemble of CONNECTED rings is of the same order of magnitude as if the rings were disconnected. 
Michael Pascaud and Gilles Montambaux