Susceptibility and Fluctuation

Abstract

Bounds are presented relating zero-field static isothermal magnetic susceptibilities to the mean-square fluctuations of corresponding magnetization variables. The lower bounds contain the first frequency moment of a spectral density. When this moment $\overline{\omega }$ approaches zero, the upper and lower bounds merge, and the susceptibility is determined by the mean-square fluctuation. In particular, if the susceptibility diverges at a temperature $T_c$, and if the expectation of the double commutator appearing in $\overline{\omega }$ is finite at and near $T_c$, then the fluctuation and the susceptibility diverge in the same manner, and their critical exponents will be identical.