Theoretical aspects of magnetic fluctuations

Abstract
The thermodynamic treatment of equilibrium fluctuations in magnetic systems is discussed and applied to a variety of situations. The spectral density of the magnetic moment or flux are derived for simply-connected bodies (sphere and cylinder) and for multiply-connected systems (loop and hollow cylinder). The material is considered to be either a normal conductor, a superconductor or ferromagnetic. The results are valid in the presence of a static magnetic field and also if the susceptibility is field-dependent. No abrupt change in fluctuations occurs as a superconductor is taken through the transition temperature. The introduction of a Josephson junction or a resistive link in a superconducting loop is shown to increase the flux fluctuations markedly with a steady increase as the link is made weaker. At high frequencies the fluctuation spectrum for a superconductor approaches that for the same system in the normal state.