Possibility of long-range order in clean mesoscopic cylinders

TL;DR

This paper investigates the potential for long-range magnetic order in clean mesoscopic cylinders by analyzing a microscopic magnetostatic interaction Hamiltonian, considering fluctuations, and determining the critical temperature for order.

Contribution

It introduces a detailed microscopic model of magnetostatic interactions in mesoscopic systems and explores conditions for long-range order beyond mean field approximation.

Findings

Identification of a critical temperature T* for ordered states.

Analysis of fluctuations affecting self-sustaining currents.

Discussion of long-range order in stacked ring systems.

Abstract

A microscopic Hamiltonian of the magnetostatic interaction is discussed. This long-range interaction can play an important role in mesoscopic systems leading to an ordered ground state. The self-consistent mean field approximation of the magnetostatic interaction is performed to give an effective Hamiltonian from which the spontaneous, self-sustaining currents can be obtained. To go beyond the mean field approximation the mean square fluctuation of the total momentum is calculated and its influence on self-sustaining currents in mesoscopic cylinders with quasi-1D and quasi-2D conduction is considered. Then, by the use of the microscopic Hamiltonian of the magnetostatic interaction for a set of stacked rings, the problem of long-range order is discussed. The temperature $T^{*}$ below which the system is in an ordered state is determined.