Magnetization of Mesoscopic Disordered Networks

TL;DR

This paper investigates the magnetic properties of mesoscopic disordered metallic networks, calculating average and typical magnetizations based on diffusion theory, revealing finite Hartree-Fock magnetization in large networks.

Contribution

It introduces a method to compute magnetization in mesoscopic networks using diffusion equations, including complex network geometries, and shows the persistence of magnetization in the thermodynamic limit.

Findings

Average magnetization remains finite in large networks.

Diffusion equations effectively model magnetic response.

Magnetization depends on network topology and electron interactions.

Abstract

We study the magnetic response of mesoscopic metallic isolated networks. We calculate the average and typical magnetizations in the diffusive regime for non-interacting electrons or in the first order Hartree-Fock approximation. These quantities are related to the return probability for a diffusive particle on the corresponding network. By solution of the diffusion equation on various types of networks, including a ring with arms or an infinite square network, we deduce the corresponding magnetizations. In the case of an infinite network, the Hartree-Fock average magnetization stays finite in the thermodynamic limit.