Magnetization of a diffusive ring: Beyond the perturbation theory

Abstract

Average persistent current over a set of diffusive metallic rings with fixed number of electrons is considered. We study the case in which the phase breaking time is much greater than an inverse average interlevel distance. In such a case, many return events for an electron must be taken into account. As a result, one arrives at a nonperturbative problem for a cooperon mode fixed by an external magnetic field. This multi-cooperon problem has been considered previously by Altland et al., [Europhys. Lett. 20, 155 (1992)] and in several following papers within the framework of supersymmetric approach. Such an approach involves very tedious calculations which were performed using a computer algebraic package. Here we solve the problem in question with the help of a replica trick. It is demonstrated that the replica trick in combination with a proper analytical continuation in the replica space allows one to obtain the result in much more explicit way.